Mr Bannon infuriated Mr Trump with comments in the book Fire and Fury describing a June 2016 meeting at Trump Tower in New York between Donald Trump Jr, Jared Kushner, Paul Manafort and a Russian lawyer where dirt on Hillary Clinton was promised as "treasonous" and "unpatriotic".
Mr Bannon said his description was aimed at former Trump campaign chairman Mr Manafort, who also attended the meeting, and not Mr Trump's son.
In a statement released to the US media, Mr Bannon described Mr Trump Jr as a patriot and a good man.
"I regret that my delay in responding to the inaccurate reporting regarding Don Jr has diverted attention from the President's historical accomplishments in the first year of his presidency," according to the statement.
Mr Bannon said his support for Mr Trump and his agenda is "unwavering".
The President's lawyers had accused Mr Bannon of defaming Mr Trump and his family and had threatened to sue him.