Former White House chief strategist Steve Bannon said in CBS interview that top Trump economic advisor Gary Cohn should have resigned after disagreeing with the president's reaction to violent protests in Charlottesville, Virginia.

"Absolutely," Bannon said when asked if Cohn should have stepped down.

"If you don't like what he's doing and you don't agree with it, you have an obligation to resign," Bannon told CBS' "60 Minutes." A segment of the interview was posted Thursday.

Cohn has said he seriously considered resigning after President Donald Trump's response to Charlottesville, saying the administration "must do better" in condemning neo-Nazis and white supremacists.

"As a Jewish-American, I will not allow neo-Nazis ranting 'Jews will not replace us' to cause this Jew to leave his job. I feel deep empathy for all who have been targeted by these hate groups. We must all unite together against them," Cohn told the Financial Times last month.

Cohn met with Trump privately in the week following the protests and even drafted a resignation letter, The New York Times reported.

Cohn leads the White House national economic council and is jointly guiding Trump's effort to enact tax reform with Treasury secretary Steve Mnuchin.

Cohn had been rumored to be Trump's pick to succeed Janet Yellen as Fed chair, but sources told The Wall Street Journal on Wednesday that the president is "unlikely" to choose him.

Read the interview on CBS News here.

— CNBC's Jacob Pramuk contributed to this report.