Gary D. Cohn, the director of the White House Economic Council, wrote a resignation letter after President Trump blamed “both sides” in the deadly protest this month against a Charlottesville, Va., rally by white supremacists and neo-Nazis, according to three people familiar with the document.

Mr. Cohn ultimately changed his mind and decided in recent days to remain on as Mr. Trump’s chief economic adviser, said one person familiar with his thinking.

But in a stunning critique of the president, Mr. Cohn told The Financial Times in an interview published on Friday that the Trump administration “can and must do better” to condemn hate groups and “do everything we can to heal the deep divisions that exist in our communities.”

Mr. Cohn is an architect of a broad set of tax reforms that the White House hopes will deliver the first legislative victory of Mr. Trump’s tumultuous administration. The president next week will travel to Springfield, Mo., in a push to sell the tax reform package.