The criticism was the first serious public condemnation of Trump's behavior by a member of his inner circle since the beginning of his presidency and raised the question of how a president who puts a heavy premium on loyalty would react.
Privately, a White House official said, Trump was furious about Cohn's public airing, though publicly, White House officials, while defending the president's response to the events in Charlottesville, acknowledged that the White House can always do more.
"Gary has not held back how he feels about the situation. He's been very open and honest, so I don't think anyone was surprised by the comments," White House press secretary Sarah Huckabee Sanders said.
At the same time, it was clear there was potential for a deterioration in the relationship between Trump and his chief economic adviser, whom he has been considering naming as Federal Reserve chair.
On Wednesday evening, Cohn complained loudly about Trump while dining with friends at a Long Island restaurant called the Frisky Oyster.
Cohn explained to his companions — in a loud voice overheard by others — that he had to be careful not to give Trump too much lead time about some new ideas because the president could disclose the information prematurely and upend the planning process, according to a person familiar with the dinner.
Cohn, a former top banker at Goldman Sachs, had been part of an internal battle in the White House over the direction of policy, often allying with the president's daughter and son-in-law, Ivanka Trump and Jared Kushner, to block proposals by Stephen K. Bannon and others who appealed to Trump's nationalist instincts. Bannon resigned last week and returned to Breitbart News, a far-right online publication.
Cohn's critics celebrated the Financial Times interview Friday, hoping that it would undercut his stature with the president. One Trump ally outside the White House, who has been strategizing to undermine Cohn, said, "Cohn looks like he blew himself up, so we're not going to have to blow him up."
Breitbart splashed the Cohn controversy on its homepage Friday: "Gary Feeds False Establishment Narrative, Mnuchin Fights It," one headline blared.
The new drama could yet again distract from the White House's plans to advance its policy priorities. Trump hopes to begin a public push to overhaul the tax code next week. Cohn and his team are playing a central role in developing the administration's strategy — as well as designing a $1 trillion infrastructure plan.
Cohn stood beside the president at Trump Tower last week at an infrastructure event as Trump defended his response to the Charlottesville violence, saying there were "very fine people" protesting with the white supremacists. While he initially did not comment, Cohn made clear — to people inside the White House and friends in New York — that he would not keep quiet about his fury over Trump's response to the violence.
Cohn drafted a resignation letter after Trump's Charlottesville remarks, but he never signed it or discussed resigning with the president, according to a person familiar with the process.
Cohn and Trump met at the president's golf resort in Bedminster, N.J., last Friday, the person said. Cohn was direct with Trump about how he felt. But he made clear in the Financial Times interview that despite his misgivings about the White House's response, he does not plan to resign.
"As a patriotic American, I am reluctant to leave my post . . . because I feel a duty to fulfill my commitment to work on behalf of the American people," Cohn told the newspaper.
Treasury Secretary Steven Mnuchin, who also is Jewish and stood with Cohn beside the president at the Trump Tower news conference, has responded differently to the president's remarks. After about 300 of Mnuchin's Yale classmates signed a public letter arguing that he had a "moral obligation" to resign, the treasury secretary issued a lengthy statement defending the president.
At Friday's White House news briefing, Mnuchin told reporters, "Under no circumstances was I going to resign."
He added that he has known Cohn for 20 years and speaks to him "every day" as they work on an overhaul of the tax code. "Gary's committed to be here," Mnuchin said.
Cohn's comments could upend Trump's decision-making over who should lead the Fed when the term of the current chair, Janet L. Yellen, expires early next year.
Trump has said he is considering reappointing Yellen, a Democrat, as well as nominating Cohn. The Fed chair is the world's most powerful bank regulator and plays a lead role in shaping the direction of the economy.
Yellen also rebuked Trump — without naming him — Friday at an annual monetary policy conference in Jackson, Wyo., saying efforts to roll back financial regulations were imprudent.
"Because of the reforms that strengthened our financial system, and with support from monetary and other policies, credit is available on good terms, and lending has advanced broadly in line with economic activity in recent years, contributing to today's strong economy," Yellen said in her speech.
Trump has called the banking regulations put in place after the financial crisis a "disaster" and has vowed to dismantle them.
"Until [Friday] morning, Gary Cohn was the overall front-runner, in my determination," to be the nominee for Fed chair, said Alan Blinder, a former Fed vice chairman. "I don't think so anymore."
Blinder said the points Cohn and Yellen were making Friday were very different. Cohn supports Trump's plan to pare back banking regulations but has drawn a line over the way the president responded to the Charlottesville violence.
Yellen's views were focused more squarely on the economy and bank oversight, and Blinder said she sent a signal that she won't be pushed into backing away from bank regulation as long as she's Fed chair.
"Janet Yellen has too much backbone," Blinder said. "She is not going to make a loyalty pledge to Donald Trump."
Trump still has time to decide whom to appoint as the next leader of the Fed, and economists think there are several other potential candidates if he decides not to pick Cohn or Yellen.
These include Kevin Warsh, a former Fed governor and senior official in the George W. Bush administration; John Taylor, a Stanford University economics professor; and Glenn Hubbard, a former Bush economic adviser and dean of the Columbia University Graduate School of Business.