NEW YORK -- Tennessee Sen. Bob Corker unleashed a harsh critique of President Trump on Thursday in reaction to the president's comments blaming "both sides" for weekend violence in Charlottesville, Virginia.

During a white nationalist rally in Charlottesville, an apparent attendee allegedly plowed a car into a group of counter-protesters, killing one woman.

Corker, the powerful chairman of the Senate Foreign Relations Committee said, in part, "the president has not yet been able to demonstrate the stability nor some of the competence that he needs to demonstrates in order to be successful."

Corker later said Mr. Trump "has also recently not demonstrated that he understands the character of this nation.

As CBS News chief Washington correspondent and "Face the Nation" moderator John Dickerson explained on Thursday's "CBS Evening News," the criticism is notable because Corker is "not one of the usual suspects who's always criticizing the president. He's been golfing with the president."

"But in this instance, he says if the president doesn't solve his problems, our nation is going to go through great peril. So where this is coming from is extraordinary and the critique he's making is a thorough one. It's not just something he tossed off," Dickerson said to CBS News' Anthony Mason.

WATCH TONIGHT: John Dickerson will appear on "The Late Show with Stephen Colbert" at 11:35 p.m. ET on CBS

Corker also called upon Mr. Trump to "move beyond himself." Dickerson says that points to a central critique of Mr. Trump that has persisted since the presidential campaign: "That his impulsiveness that made him so popular among his base is incompatible with the office he holds."

"So when [Corker] talks about the lack of discipline, the lack of stability, those are central, elemental characteristics the president has to have. And Sen. Corker is saying that they are not there in the president now," Dickerson said.

John Dickerson CBS News

Despite the recent staff shakeups at the White House, Dickerson says, the criticism is aimed at only the president, and "there is no amount of staff you can ring around a president to fix" the problems as Sen. Corker has identified.

"He calls on the president to have some self-reflection, so if you're in the White House you have to hope the president is listening," Dickerson said.