"You can tell him, 'Hey, maybe you can do it a better way'," Bannon said in an interview with "60 Minutes." "But if you're going to break, then resign. If you're going to break with him, resign."
Bannon reiterated his position when asked to clarify if he was talking about Cohn.
"So Gary Cohn should have resigned?" Rose said.
"Absolutely," Bannon replied.
In an interview with the Financial Times, Cohn condemned Trump's remarks that appeared to equate white-nationalist ralliers in Charlottesville with counterprotesters. One of the counterprotesters was killed after a car plowed through a crowd during the rally.
"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," Cohn told the FT.
Trump held a fiery press conference a few days after the violence in Charlottesville — one that reportedly left Cohn "disgusted" and "appalled."
Those reports, Bannon said, were proof that Cohn should have left his job.
"The stuff that was leaked out that week by certain members of the White House I thought was unacceptable," Bannon. "If you find it unacceptable, you should resign."
Cohn's disagreement with Trump appears to have already taken a toll on his standing in the White House, as The Wall Street Journal reported on Wednesday that the former Goldman Sachs (NYSE:GS) COO is no longer the front-runner to be the next chairman of the Federal Reserve because of his criticism.
Watch Bannon's comments: