This has been CNBC's live blog covering updates on the war in Ukraine. [Follow the latest updates here.]

Russia continues to press its allegation that Ukraine plans to use a so-called "dirty bomb" on its own territory, and says it will take it up with the United Nations. Ukrainian and Western officials have denounced the claim as a "pretext for aggression."

Kyiv has requested a team from the U.N.'s watchdog agency to inspect its nuclear power facilities in order to disprove Moscow's claims.

A "dirty bomb" is made to contaminate a large area with radioactivity, making it harmful or uninhabitable for residents there, without using a nuclear explosion.

Meanwhile, a Russian court denied WNBA star Brittney Griner's appeal after the American athlete was convicted on drug charges earlier this year.

Infrastructure bottlenecks hamper Russia's booming coal exports to China: Reuters

Russian coal exports to energy-hungry China have jumped by about a third this year but the supply boom is being constrained by transport infrastructure limitations, industry sources and officials said.

China is seeking coal supplies from overseas, in particular after recent Covid-19 outbreaks in the major coal mining regions of Inner Mongolia and Shaanxi forced many mines to close, while coal demand at power generation and heating sectors will soon pick up with the coming of winter.

The Kremlin plans to increase its energy supplies to Asia, China in particular, to offset a slump in exports to the West, which has imposed sanctions on Russia over the conflict in Ukraine.

Russia is the world's sixth-largest coal producer and one of top coal exporters, along with Indonesia and Australia. Its share of global coal exports reached 17% last year with supply of 223 million tons.

— Reuters

At least 10 million people will need psychosocial support from Russia's war in Ukraine, WHO says

Ukraine's Ministry of Health and WHO report that at least 10 million people will need psychosocial support due to the trauma from Russia's conflict in Ukraine.

"This includes women and girls suffering sexual violence and other forms of gender-based violence, children hearing warning sirens daily, families who have been separated, or people just trying to survive every day," explained Denise Brown, the U.N. Resident Coordinator in Ukraine, said in remarks before the United Nations Security Council.

Brown added that civilians in recently liberated areas of Ukraine are particularly vulnerable as they have "witnessed or experienced terrible violations" committed by Russian forces.

— Amanda Macias

WHO records more than 630 attacks on vital health services in Ukraine since the start of Russia’s invasion

Since Russia invaded Ukraine on Feb. 24, there have been at least 631 attacks on vital health services in the country, the World Health Organization's Surveillance System for Attacks on Health Care estimates.

The organization reports that healthcare facilities were damaged 549 times, ambulances were targeted in 82 cases and at least 158 attacks affected crucial medical supplies. The group also estimated that attacks on health services led to at least 100 deaths and 129 injuries.

The Kremlin has previously denied that it targets civilian infrastructure like hospitals, schools and apartment buildings.

— Amanda Macias

More than 7.7 million Ukrainians have become refugees from Russia's war, U.N. estimates

More than 7.7 million Ukrainians have become refugees and moved to neighboring countries since Russia invaded Ukraine in late February, the U.N. Refugee Agency estimates.

Nearly 4.4 million of those people have applied for temporary resident status in neighboring Western European countries, according to data collected by the agency.

"The escalation of conflict in Ukraine has caused civilian casualties and destruction of civilian infrastructure, forcing people to flee their homes seeking safety, protection and assistance," the U.N. Refugee Agency wrote.

— Amanda Macias

Seven ships carrying more than 220,000 metric tons of agricultural products to leave Ukraine

The organization overseeing the export of grain from Ukraine said it has approved seven vessels to leave the besieged country.

The Black Sea Grain Initiative, a deal announced in July among Ukraine, Russia, the United Nations and Turkey, said the vessels are carrying a total of 224,850 metric tons of grain and other crops.

The seven ships will leave Ukraine's port of Odesa, Chornomorsk and Yuzhny-Pivdennyi for Spain, China, Romania, Greece and The Netherlands.

Read more about the Black Sea Grain Initiative here.

— Amanda Macias

Ukrainian official asks Ukrainians abroad to not return home and to stay abroad

Ukraine's deputy prime minister Iryna Vereshchuk asked Ukrainians who are currently abroad to not return home yet, according to an NBC News translation.

"I will ask you not to return, we have to survive the winter," Vereshchuk said, adding that Ukraine's energy sector and infrastructure is too weak from the war to provide adequate support.

"If there is an opportunity to stay, for the time being, spend the winter abroad," she added.

In recent weeks, Russian missiles and drone strikes have targeted critical Ukrainian infrastructure like energy systems. The Kremlin has previously denied Ukrainian and Western claims that it targets civilian infrastructure, which is a violation of the laws of conflict.

— Amanda Macias

White House says it would be a 'major mistake' for Russia to use nuclear weapons

White House Press Secretary Karine Jean-Pierre said it would be "a major mistake" for Russia to use nuclear weapons in Ukraine and that it is taking the threat of a dirty bomb seriously.

"It would be a major mistake for Russia to use nuclear weapons in Ukraine leading to severe consequences," Jean-Pierre said at the daily briefing.

The statement came in response to a question about the potential for Russia to use a dirty bomb. Russia has accused Ukraine of planning to use a "dirty bomb" on its own territory. On Tuesday Russia reiterated the allegations in a letter to the United Nations Security Council.

"We must take this seriously because in the past we have seen Russia use allegations as a pretext to escalate."

— Emma Kinery

Two NATO allies still have to approve Sweden and Finland’s entry into the alliance

Two NATO member countries have yet to sign ratification protocols for Finland and Sweden to join the military alliance.

Out of NATO's 30 member countries, Hungary and Turkey are the last holdouts to grant Sweden and Finland membership. Slovakia was the latest NATO ally to sign ratification documents on September 27.

In May, both nations began the formal process of applying to NATO as Russia's war in Ukraine raged. All 30 members of the alliance have to ratify the countries' entry into the group.

In August, U.S. President Joe Biden signed ratification documents following a 95-1 Senate vote to bring Finland and Sweden into NATO.

NATO Secretary General Jens Stoltenberg said last week during a meeting with Swedish Prime Minister Ulf Kristersson that the process of adding Sweden and Finland to the alliance is the "fastest in NATO's modern history."

— Amanda Macias

White House calls on Russia to 'negotiate in good faith' on Griner release

The White House called on Russia to "negotiate in good faith" as the Biden administration works for the release of WNBA star Brittney Griner.

White House press secretary Karine Jean-Pierre referenced an offer it made in August to the Russian government for the release of Griner and the former U.S. Marine Paul Whelan.

Whelan was arrested in 2018 on charges of acting as a spy for the United States. At the time he was arrested, Whelan was visiting Russia to attend a wedding, according to his brother, David Whelan. 

Jean-Pierre added that the Biden administration is still working behind the scenes through diplomatic channels to broker the immediate release of Griner and others wrongfully detained abroad.

Earlier on Tuesday, a Russian court upheld Griner's nine-year prison sentence, a decision that will send the U.S. athlete to a penal colony.

— Amanda Macias

Blinken meets with IAEA chief amid Russian 'dirty bomb' allegations

Secretary of State Antony Blinken spoke with IAEA director general Rafael Mariano Grossi about the situation at the Russian-occupied Zaporizhzhia nuclear power plant.

"Secretary Blinken expressed appreciation for the IAEA's efforts to help ensure the safety and security at Ukraine's Zaporizhzhia nuclear power plant," according to a State Department readout of the meeting.

Blinken also welcomed the nuclear watchdog agency's readiness to visit Ukraine in the wake of Russia's false "dirty bomb" allegations.

— Amanda Macias

Biden says Russia's use of a nuclear weapon would be 'an incredibly serious mistake'

U.S. President Joe Biden said Russia would be making "an incredibly serious mistake" if Moscow used a tactical nuclear weapon in its fight with Ukraine.

"I'm not guaranteeing that it's a false flag operation," Biden said, referencing Russian allegations that Ukraine is planning on using a "dirty bomb" in order to escalate the conflict.

"It would be a serious serious mistake," Biden added.

The United States and Russia hold the lion's share of the world's nuclear weapons.

Both the Pentagon and State Department said that they were closely monitoring Russia's rhetoric which it described as "reckless" and "irresponsible."

"At this time, we haven't seen any reason to adjust our own nuclear posture, nor do we have indications that Russia is preparing to use nuclear weapons,"  State Department spokesman Ned Price told reporters during a daily press briefing.

— Amanda Macias

Biden says his administration is in regular contact with Russian authorities on WNBA star Griner's case

U.S. President Joe Biden said his administration is in regular contact with Russian authorities on behalf of WNBA star Brittney Griner following a Russian court's decision to deny an appeal of her 9-year prison sentence.

"So far we have not been met with much response but we're not stopping," Biden said, referencing a U.S. offer to the Russian government for the release of Griner and former U.S. Marine Paul Whelan.

Biden also added that his administration was working to get all Americans wrongfully detained abroad back home.

Earlier on Tuesday a Russian court upheld Griner's sentence, a decision that will send the two-time Olympic gold medalist to a penal colony.

Griner has about eight years left on her sentence though another appeal is possible through Russia's highest court of appeals. It is not clear if she will pursue another appeal.

— Amanda Macias

Democrats retract letter asking Biden to negotiate directly with Putin

A group of 30 progressive Democrats that signed a letter asking U.S. President Joe Biden to directly negotiate with Russian President Vladimir Putin have retracted the note.

The two-paged letter signed by Progressive Caucus Chair Pramila Jayapal, D-Wash., Reps. Jamie Raskin, D-Md., Ilhan Omar, D-Minn., Ro Khanna, D-Calif., and others called for a renewed diplomatic push, including direct talks with the Kremlin in order to end the conflict in Ukraine.

In a statement on Tuesday, Jayapal said the letter was released by mistake.

"The letter was drafted several months ago, but unfortunately was released by staff without vetting. As Chair of the Caucus, I accept responsibility for this," she added.

— Amanda Macias

Pope, other leaders, appeal for end to 'nuclear nightmare'

Pope Francis joined other religious leaders at Rome's Colosseum to make a plea for peace and ending what they called the "nuclear nightmare" as fears intensify that Russia's war against Ukraine may see atomic weapons used.

A ceremony at the ancient Roman arena capped a conference on promoting world peace. The Sant'Egidio Community, a Catholic charity with close ties to the Vatican, organized the three-day event in Italy's capital.

In remarks to participants, Francis noted that Pope John XXIII urged government leaders exactly 60 years ago, during the U.S.-Russian Cuban missile crisis, to spare the world from a nuclear holocaust.

"Sixty years later, these words still impress us with their timeliness,'' Francis said. "I make them my own."

"Today peace has been gravely violated, assaulted and trampled upon, and this in Europe, on the very continent that in the last century endured the horrors of two world wars." the pope lamented.

— Associated Press

30 Democrats send letter to Biden asking for direct talks with Putin to end conflict

A group of 30 progressive Democrats in Congress have signed a letter asking U.S. President Joe Biden to directly engage with Russia in order to bring an end to the conflict in Ukraine.

The two-paged letter signed by Progressive Caucus Chair Pramila Jayapal, D-Wash., Reps. Jamie Raskin, D-Md., Ilhan Omar, D-Minn., Ro Khanna, D-Calif., and others calls for a renewed diplomatic push, including direct talks with the Kremlin.

"If there is a way to end the war while preserving a free and independent Ukraine, it is America's responsibility to pursue every diplomatic avenue to support such a solution that is acceptable to the people of Ukraine," the letter reads.

"Such a framework would presumably include incentives to end hostilities, including some form of sanctions relief, and bring together the international community to establish security guarantees for a free and independent Ukraine that are acceptable for all parties, particularly Ukrainians."

— Amanda Macias

Blinken speaks to his Ukrainian counterpart amid Russian 'dirty bomb' claims

U.S. Secretary of State Antony Blinken spoke with his Ukrainian counterpart and reaffirmed U.S. support amid false Russian claims that Kyiv was preparing to use a "dirty bomb."

"He noted our commitment to work with allies and partners to continue meeting Ukraine's security assistance needs on the battlefield," State Department spokesman Ned Price said in a statement.

Earlier this week, the Kremlin said Ukraine plans to use a so-called "dirty bomb" on its own territory in order to blame Russia and escalate the conflict further. Ukrainian and Western officials have denounced the claim as a "pretext for aggression."

— Amanda Macias

Griner's attorney says WNBA star has lost hope

Brittney Griner's attorney Maria Blagovolina said the basketball star will have to decide whether to make a last effort to appeal her sentence, but today's decision has caused her to lose hope.

Griner has about eight years left on her sentence though another appeal is possible through Russia's court of cassation, the highest court of appeals. It is not clear if her lawyers will pursue another appeal.

"We think we should use all legal tools available but that is her decision to take," Blagovolina told reporters outside of the court. She added that the two-time Olympic gold medalist was disappointed to hear the decision from the three-judge panel.

"She had some hope but that vanished today," Blagovolina said.

— Amanda Macias

Russian court rejects Brittney Griner's appeal

A Russian court rejected Brittney Griner's appeal after the U.S. basketball star was convicted on drug charges earlier this year and sentenced to nine years in jail.

Read the full story here.

— Sam Meredith

Russian appeal court prosecutor says 9-year sentence for Brittney Griner is 'fair'

The Russian state prosecutor in U.S. WNBA star Brittney Griner's appeal hearing told the judges presiding over her case that the nine-year jail term for possession and smuggling of drugs was "fair," according to Reuters.

Griner, who was convicted on drug charges earlier this year, was seen listening via video link to a live translation of the proceedings from a detention center just outside Moscow.

A lawyer for Griner said her nine-year jail term was excessive and asked the court to acquit her, Reuters reported.

Griner's lawyers told NBC News before the hearing that the two-time Olympic gold medalist was "quite pessimistic" that the judge will overrule the court's original verdict.

— Sam Meredith

New UK PM Sunak says Ukraine war must be seen successfully to its conclusion

Rishi Sunak said in his first speech as British prime minister that the Ukraine war must be seen successfully to its conclusion.

"I understand how difficult this moment is after the billions of pounds it cost us to combat Covid, after all the dislocation that caused in the midst of a terrible war that must be seen successfully to its conclusions," Sunak said from outside 10 Downing Street.

"I fully appreciate how hard things are," he added.

Meanwhile, French President Emmanuel Macron congratulated Sunak on becoming Britain's new prime minister, saying via Twitter he would look forward to working with him on common challenges such as the war in Ukraine.

— Sam Meredith

German president pays surprise visit to Kyiv

German President Frank-Walter Steinmeier paid a surprise visit to Kyiv Tuesday, his first since the Russian invasion began on Feb. 24.

In what appeared to be an effort to redeem himself, Steinmeier stressed his support for Ukraine after previously facing criticism from Kyiv for his erstwhile role in creating closer economic ties between Russia and Germany.

"My message to Ukrainians: you can count on Germany," the president said.

In the months since the war began, Steinmeier expressed regret for his work with Russia, saying in early April, "My sticking to ... Nord Stream 2, that was definitely a mistake. We held on to bridges that Russia no longer believed in, and of which our partners warned us." Nord Stream 2 was a multi-billion dollar Baltic sea pipeline project that would have enabled more Russian gas to flow to Germany. The project was suspended in the days leading up to Russia's invasion.

— Natasha Turak

All remaining men in occupied Kherson encouraged to join Russian-backed militia

The remaining men in occupied Kherson are being encouraged to join a new local Russian-backed militia that would fight the incoming Ukrainian forces that have gradually been taking back land.

Russian authorities are urging civilians to leave the territory as Ukrainian forces approach, and say that 25,000 residents have left in the last week.

It's not clear if the men remaining in the Kherson are being forced to fight on the Russian side, but making civilians serve in the armed forces of an occupying country is considered a violation of the Geneva Convention.

Kherson is one of four territories in eastern Ukraine that was illegally annexed by Russia in late September.

— Natasha Turak

Russia to raise Ukraine 'dirty bomb' accusation at U.N., diplomats say

Russia intends to raise at the United Nations Security Council on Tuesday its accusation that Ukraine is planning a "dirty bomb" attack and has urged U.N. chief Antonio Guterres to do all he can to "prevent this heinous crime from happening."

"We will regard the use of the 'dirty bomb' by the Kiev regime as an act of nuclear terrorism," Russia's U.N. Ambassador Vassily Nebenzia wrote in a letter - seen by Reuters - to Guterres and the Security Council.

"We urge the Western countries to exert their influence on the regime in Kiev to abandon its dangerous plans threatening international peace and security," he wrote. "We call on the Secretary-General of the United Nations to do everything in his power to prevent this heinous crime from happening."

With Ukrainian forces advancing into the strategic Russian-occupied province of Kherson, top Russian officials phoned Western counterparts on Sunday and Monday to tell them Moscow suspected Ukraine of planning to use a so-called "dirty bomb" laced with nuclear material.

Ukrainian President Volodymyr Zelenskyy has responded by accusing Russia of planning such an attack itself to blame on Ukraine. Western countries also rejected Russia's allegation as a pretext for intensifying the eight-month-long war, which began in February when Russian forces invaded neighboring Ukraine.

Russia has told council counterparts it will bring up the issue during a closed-door meeting on Tuesday, diplomats said.

— Reuters

Safeguards inspectors to visit two nuclear locations in Ukraine, IAEA’s Grossi says following requests from Ukraine

The International Atomic Energy Agency will visit two nuclear locations in Ukraine, following a request from Ukrainian Foreign Minister Dmytro Kuleba to disprove Russian allegations that Ukraine plans to use a "dirty bomb."

"The IAEA inspected one of these locations one month ago and all our findings were consistent with Ukraine's safeguards declarations," IAEA Director General Rafael Mariano Grossi said in a statement. "No undeclared nuclear activities or material were found there."

Both sites are under the U.N. nuclear watchdog's safeguards and receive regular visits from IAEA regulators, according to the agency. The IAEA said the purpose of the upcoming visit is to detect any undeclared nuclear activities or materials that could be consistent with Russia's "dirty bomb" allegations.

— Rocio Fabbro

World Bank provides Ukraine with additional $500 million

The World Bank has distributed another $500 million to Ukraine to help finance the country's critical spending needs.

The financing, provided by its lending arm, the International Bank for Reconstruction and Development, had been supported by $500 million in loan guarantees from the United Kingdom that were announced on Sept. 30, the bank said.

In total, the bank said it has authorized $13 billion in emergency financing for Ukraine, of which $11.4 billion has been distributed.

A report published in September by the World Bank, the Ukrainian government and the European Commission estimated reconstruction and recovery costs totaled $349 billion as of June 1. However, the number is expected to keep increasing as the war drags on.

— Natalie Tham

Read CNBC's previous live coverage here:

U.S. denounces Russia's 'dirty bomb' claim; more than a million Ukrainian homes have lost power