"I tweeted something highly inappropriate and vulgar about the president and his family in response to the devastating images I was seeing on television".
But he also added that, like every other American, concerned about the situation of children separated from their families on the US border.
Fonda's Wednesday tweet came amid a storm of criticism against the Trump administration over its "zero tolerance" policy regarding immigrants, which has separated more than 2,300 children from their parents at the border since being put into action months ago.
Fonda, who is the younger brother of Oscar victor Jane Fonda, initially tweeted early Wednesday morning about the migrant crisis, hours before Trump signed an executive order reversing his own policy of separating families at the border.
Donald Trump Jr., who repeatedly called on Sony Pictures to denounce Fonda, suggested that the company's decision to still release the film, in which Fonda plays a supporting role, pointed to a double standard between conservative and liberal responses to culture controversies. It was wrong and I should not have done it.
A spokesman for Sony Pictures Classics, referring to the indie feature Boundaries which is set to open Friday, said: "Peter Fonda's comments are abhorrent, reckless and risky, and we condemn them completely. I immediately regretted it and sincerely apologise to the family for what I said and any hurt my words have caused".
This is in keeping with the Fonda family values, sister Jane has quite a history.
President Donald Trump, first lady Melania Trump, and their son and Barron Trump walk from Marine One across the South Lawn to the White House in Washington, June 11, 2017, as they return from Bedminster, N.J.
"To pull or alter this film at this point would unfairly penalise the filmmaker Shana Feste's accomplishment, the many actors, crew members and other creative talent that worked hard on the project".
Sony added in its statement that the movie will debut as scheduled with a "limited release of five theaters".