• The District of Columbia's attorney general said he is looking at whether to charge Donald Trump Jr., Rudy Giuliani and Rep. Mo Brooks with inciting the violent invasion of the U.S. Capitol.
• The attorney general, Karl Racine, also left open the door to prosecuting President Trump himself for the same conduct once he leaves office later this month.
• Brooks, in his speech at the rally, had said: "Today is the day American patriots start taking down names and kicking ass."

The District of Columbia's attorney general said Monday that he is looking at whether to charge Donald Trump Jr., Rudy Giuliani and U.S. Rep. Mo Brooks with inciting the violent invasion of the U.S. Capitol last week by a horde of President Donald Trump's supporters.

Karl Racine also left open the door to prosecuting President Trump himself for the same conduct once he leaves office later this month.

Racine's comments came during an interview on MSNBC's "Andrea Mitchell Reports," after he was shown video clips of the Trumps and the president's personal lawyer, Giuliani, whipping up a crowd at a rally outside the White House last Wednesday, and asked about the trio and Brooks, an Alabama Republican.

Both Trumps had urged the crowd to fight, and Giuliani had called for "trial by combat," as they falsely claimed that Joe Biden had been declared the victor of the the presidential election because of ballot fraud.

Brooks, in his speech at the rally, had said: "Today is the day American patriots start taking down names and kicking ass," and asked the throng if they were "willing" to sacrifice their blood or lives as their ancestors had done.

After the rally, a mob of Trump supporters invaded the Capitol, killing one Capitol Police officer, swarming through the halls, looting offices and disrupting the session of Congress that was being held to confirm Biden's election.

"Let's just say first, those were outrageous comments that those individuals, including the president of the United States made," Racine said.

"Clearly the crowd was hyped up, juiced up, focused on the Capitol and rather than calm then down or at least emphasize the peaceful nature of what protests need to be, they really did encourage these folks and riled them up," Racine said.

"Whether that comes to a legal complaint, I think we've got to really dig in and get all of the facts. I know I'm looking at a charge under the D.C. Code of inciting violence, and that would apply where there's a clear recognition that one's incitement could lead to foreseeable violence," the attorney general said.

"We still have more investigation to do, and that's what we're going to do. We're going to work zealously and fully and let the facts lead to where they naturally go."

Racine noted that the U.S. Justice Department has claimed it cannot prosecute a sitting president while in office.

"As it turns out, the president has about nine more days of office and, of course, the investigation is going to go on much beyond those nine days," Racine said.

"It will be another legal question as to whether the president can be prosecuted after his term of office. I think the better weight of authority answers that question affirmatively. And I'm not targeting the president or anyone else."

CNBC has reached out for comment from the Trumps, Giuliani and Brooks.