Redford's Sundance Institute supports the festival
The actor was speaking at the start of the Sundance Film Festival in Utah, where the opening movie recalled protests over the Vietnam war in 1968.
Redford said he, like many others, had shown a "spirit of unity" with the US government after 11 September 2001.
"We put all our concerns on hold to let the leaders lead," he said. "I think we're owed a big, massive apology."
The actor, whose Sundance Institute for independent film runs the annual festival, usually steers clear of political messages in his opening speech.