In a tweet on Wednesday night, Mr. Trump urged supporters to “join me” at a campaign rally scheduled for Aug. 22 in Phoenix. But the Phoenix mayor, Greg Stanton, said in his own tweet that he was “disappointed” that the president would hold a political event “as our nation is still healing from the tragic events in Charlottesville.” He urged Mr. Trump to delay the visit.

The president’s top advisers described themselves as stunned, despondent and numb. Several said they were unable to see how Mr. Trump’s presidency would recover, and others expressed doubts about his capacity to do the job.

In contrast, the president told close aides that he felt liberated by his news conference. Aides said he seemed to bask afterward in his remarks, and viewed them as the latest retort to the political establishment that he sees as trying to tame his impulses.

Mr. Trump’s venting on Tuesday came despite pleas from his staff, including his daughter Ivanka Trump and her husband, Jared Kushner. Instead of taking their advice to stop talking about the protest, the president eagerly unburdened himself of what he viewed as political correctness in favor of a take-no-prisoners attack on the “alt-left.”

On Wednesday, even Fox News, a favorite of the president’s, repeatedly carried criticism of Mr. Trump. One Fox host, Shepard Smith, said that he had been unable to find a single Republican to come on-air to defend Mr. Trump’s remarks.

No one from the president’s team has resigned as of yet, but some spoke candidly on Wednesday about whether they could continue to work much longer for a man who has expressed such sentiments. Most incensed among Mr. Trump’s top advisers, according to three people familiar with the situation, was Gary D. Cohn, the director of the National Economic Council, who told people around him that he was offended, as a Jew and as an American, by the president’s reaction to the violence in Charlottesville.

The relationship between the president and Mr. Cohn, who stood next to Mr. Trump during the news conference, seems to have suffered a serious blow. Although White House aides denied that he was planning to quit, they acknowledged that Mr. Cohn, a former Goldman Sachs executive, was upset with the president’s lack of discipline.