A prominent Jewish member of President Trump's administration said that the White House "can and must do better" in consistently condemning hate groups.

The sharp critique from Mr. Trump's top economic adviser, Gary D. Cohn, came nearly two weeks after deadly violence in Charlottesville, Va., in response to a rally led by white nationalist groups. Mr. Cohn, who is Jewish, seriously considered resigning and even drafted a letter of resignation, according to two people familiar with the draft.

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In his first public remarks on the national dialogue about the violence, Mr. Cohn said in an interview on Thursday with the Financial Times, that as a "patriotic American" he did not want to leave his job as the director of the national economic council. "But I also feel compelled to voice my distress over the events of the last two weeks," Mr. Cohn said.

In the days after the Charlottesville rally, when Mr. Trump defended white nationalist protesters, Jewish members of the administration were mostly silent. Mr. Cohn is so far one of the few in the administration to publicly condemn the president's remarks. Military leaders posted messages on social media denouncing neo-Nazis and racism, but did not specifically mention the commander in chief. Public deviation from the president by the military is unusual.

Mr. Trump said there were "very fine people on both sides," as Mr. Cohn stood nearby in the lobby of Trump Tower where the president made his remarks to reporters. After Mr. Trump left, Mr. Cohn stood uncomfortably fielding questions about the president's statements, and he repeatedly declined to comment. At the time, people close to Mr. Cohn said he was disgusted and deeply upset by Mr. Trump's comments.

On Thursday, Mr. Cohn spoke publicly for the first time about the issue in the Financial Times interview, which largely focused on tax reform.

"Citizens standing up for equality and freedom can never be equated with white supremacists, neo-Nazis, and the K.K.K.," Mr. Cohn said. "I believe this administration can and must do better in consistently and unequivocally condemning these groups and do everything we can to heal the deep divisions that exist in our communities."

Mr. Cohn added, "As a Jewish American, I will not allow neo-Nazis ranting 'Jews will not replace us' to cause this Jew to leave his job."

Mr. Cohn's decision to publicly distance himself from the president comes at an awkward time, as Mr. Trump prepares next week to start a major national effort to sell a tax-cut plan, which Mr. Cohn has been toiling for months behind the scenes to craft. The president will travel to Springfield, Mo., to begin that push, a White House official said on Friday, the first of a series of stops around the country to build support for a major tax reduction, which Mr. Trump has vowed to enact this year though he has released few details.

In the days after the Charlottesville violence, Mr. Cohn's family — including his wife — told him he needed to think seriously about departing, according to two people briefed on the discussions. Several of his friends in the business community also urged him to step away from the administration. Mr. Cohn is a former executive at Goldman Sachs.

Mr. Cohn came close to resigning, according to one of the people briefed on the discussions. He met with Mr. Trump privately at the president's golf club in New Jersey last Friday, scrapping his plans to spend the evening at his second home in the Hamptons.

The markets were spooked last week amid fears that Mr. Cohn would resign, and United States stocks dropped until the White House denied the rumor. Mr. Cohn, who had spent his entire career in the trading world before joining Mr. Trump late last year, was deeply troubled by the market reaction, people close to him said.

Mr. Cohn also told the Financial Times he spoke privately with Mr. Trump about these issues.

"I have not been bashful saying what I think," Mr. Cohn said.

Mr. Cohn is known to be interested in becoming chairman of the Federal Reserve, and still sees that as a possibility. It was not clear whether he told the president he planned to speak to the Financial Times.

Mr. Cohn's remarks were in stark contrast to a statement from the Treasury secretary, Steven Mnuchin, who defended the president. Mr. Mnuchin is also Jewish.