"What you saw the other day was as serious as it can get. This is a direct attack on the institutions," Bannon said during a flying visit to Italy. "This is a coup, okay".
The column was published on Wednesday and was written by an unnamed senior administration official, the New York Times said.
The writer slammed Trump's "amorality" and said: "Many of the senior officials in his own administration are working diligently from within to frustrate parts of his agenda and his worst inclinations."
Bannon said the last time a U.S. president had been challenged in such a fashion was during the American Civil War when General George B. McClellan clashed with the then president, Abraham Lincoln.
"This is a crisis. The country has only ever had such a crisis in the summer of 1862 when General McClellan and the senior generals, all Democrats in the Union Army, deemed that Abraham Lincoln was not fit and not competent to be commander in chief," Bannon said.
Trump said on Friday the U.S. Justice Department should find out who wrote the piece, adding that it was an issue of national security.
Bannon was fired by Trump in August, 2017 after he fell out with the president's more mainstream advisers over his efforts to bend the Republican party to his own economic nationalist agenda.
Bannon said he had resigned from his post and told CBS television at the time that the "Republican establishment" was looking to nullify the 2016 election and neuter Trump.
"There is a cabal of Republic establishment figures who believe Donald Trump is not fit to be president of the United States. This is a crisis," Bannon said in Rome.
"I am not a conspiracy guy ... I have said there is no deep state. It is an in-your-face state."
He warned liberal progressives within the Democratic Party, such as Bernie Sanders, not to take any pleasure in the White House turmoil."Don't think it will be any different if you take power. Because this is the established order dictating that they know better than the people," he said.