While he later expanded his comments on August 14 to mention neo-Nazis and the Ku Klux Klan, the president claimed there were "very fine people" among the white nationalists in a raucous Trump Tower press conference in which Cohn stood next to him.
After the rally - which ended in a neo-Nazi killing a woman after ramming his vehicle into a crowd of counter-protesters - Trump said "both sides were to blame" for the rally's violence and that "very fine people" were marching with neo-Nazis.
"I have come under enormous pressure both to resign and to remain in my current position", the former banker told the British daily.
"Starting next week the president's agenda and calendar is going to revolve around tax reform", Cohn said.
Trump's comments also led to the quick dissolution of two groups of prominent corporate advisers, many of whom felt they could no longer be associated with a president who didn't rapidly and unequivocally condemn neo-Nazis and white supremacists. "Cohn should announce that Janet Yellen is the most qualified candidate for the job of Fed Chair and resign from the Trump's Director of the National Economic Council".
Cohn is one of Trump's closest advisers and is responsible for trying to shepherd the White House's entire economic policy platform - tax cuts, infrastructure spending, health care changes - into law.
Cohn said that, despite pressure, he would not leave his White House role.
Gary Cohn, Trump's top economic adviser, told the Financial Times in an interview that members of congressional committees with purview over the issue will be making numerous calls when it comes to tax reform.
Judge orders Dreamhost to turn over inauguration protest website data
The two parties are set to meet in court on Thursday, having already delayed a hearing originally scheduled for last week. Dreamhost took the Department of Justice to court to challenge the scope of that request.
It's unclear how Trump will respond to these comments from Cohn.
"I am reluctant to leave my post as director of the National Economic Council because I feel a duty to fulfill my commitment to work on behalf of the American people. But I also feel compelled to voice my distress over the events of the last two weeks".
After Trump left the press conference, Cohn was asked directly about the white supremacists who have supported Trump. "I can tell you I'm speaking to him every day", he said.
"I think there is no question the president was not equating the hate groups with people who were [protesting] peacefully", Mnuchin said.
In a statement Sunday, Mnuchin said, "I strongly condemn the actions of those filled with hate and with the intent to harm others".
"Citizens standing up for equality and freedom can never be equated with white supremacists, neo-Nazis, and the KKK", Cohn told the Financial Times.
"Gary and I have known each other for 20 years. his No. 1 focus is absolutely working on tax reform with me and getting tax reform done", Mnuchin said.
Tax reform was one of the major promises that the Trump campaign was built on, with the Republican pledging to lower corporation tax to 15% in an effort to create more jobs domestically.