Mr. Trump will continue to receive regular updates from his team, according to the official to whom the statement was attributed, and Thomas P. Bossert, the White House homeland security adviser, was in Bedminster monitoring the situation.
Mr. Bossert, in an interview Sunday on CNN’s “State of the Union,” dismissed any suggestion that the president had failed to adequately condemn white supremacists.
Mr. Bossert praised the statement the president made on Saturday — which denounced the “egregious display of hatred, bigotry and violence on many sides” — saying that Mr. Trump had appropriately criticized an event that “turned into an unacceptable level of violence at all levels.”
“This isn’t about President Trump — this is about a level of violence and hatred that could not be tolerated in this country,” Mr. Bossert told CNN’s Jake Tapper. “I was with the president yesterday, and I’m proud of the fact that he stood up and calmly looked into the camera and condemned this violence and bigotry in all its forms. This racial intolerance and racial bigotry cannot be condoned.”
Mr. Tapper responded by citing a white nationalist website that described Mr. Trump’s remarks as “really, really good.” He then asked Mr. Bossert: “Are you at least willing to concede that the president was not clear enough in condemning white supremacy?”
Mr. Bossert replied that Mr. Trump “didn’t dignify the names of these groups of people, but rather addressed the fundamental issue.”
Mr. Trump consulted a broad range of advisers before speaking on Saturday, most of whom told him to sharply criticize the white nationalist protesters. The president listened attentively, according to a person familiar with the discussions, but repeatedly steered the conversation back to the breakdown of “law and order,” and the responsibility of local officials to stem the violence.
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Two Virginia state troopers who were involved in the response to the violence died when their helicopter crashed in a wooded area near the campus on Saturday.
As the gravity of the events on Saturday became clearer, the pressure on Mr. Trump to make a stronger statement came from his innermost circle of advisers and family.
“With the moral authority of the presidency, you have to call that stuff out,” Anthony Scaramucci, an ally of Mr. Trump’s who served briefly as White House communications director last month, told George Stephanopoulos of ABC’s “This Week” on Sunday.
“I wouldn’t have recommended that statement,” added Mr. Scaramucci, whose abbreviated tenure was characterized by a pledge to let Mr. Trump express himself without interference from staff members. “I think he would have needed to have been much harsher.”
Mr. Scaramucci, a New York hedge fund executive, blamed the influence of Mr. Trump’s embattled chief strategist, Stephen K. Bannon, who ran Breitbart News, a website that attracted a substantial following among white nationalists.
Mr. Scaramucci said there was a “sort of Bannon-bart influence” that “is a snag on the president.”
Still, the tone and tenor of the president’s comments on Saturday — noticeably less fiery than what he has had to say on Twitter and in public settings about the North Korean leader, Kim Jong-un, and the Senate majority leader, Mitch McConnell — reflected Mr. Trump’s own thinking.
And the episode again proved the limitations of Mr. Trump’s family, which was once expected to exert a moderating influence on his presidency.
Ivanka Trump, a senior adviser to her father, used Twitter early Sunday to denounce the violence in Charlottesville, becoming the highest-ranking administration official to condemn the protesters on the record.
“There should be no place in society for racism, white supremacy and neo-nazis,” she wrote Sunday.