The Bush administration wanted to keep the film off screens in the run-up to November's US election, Moore alleged on Sunday.
The movie, to be screened on Monday, investigates the reasons for the Iraq war and suggests connections between the Bush and Bin Ladin families.
Moore has given no evidence to substantiate his allegations, but said "someone connected to the White House" and a "top Republican" had put pressure on film companies not to release the film.
A best-selling novelist, Moore had already gone on the record as saying film studio Disney refused to distribute his film for political reasons.
But Disney accused Moore of engineering a dispute about the film's release to gain maximum publicity.
It said it had blocked the film because it wanted to be impartial during the election, but strongly denied coming under any outside pressure.
"It is certainly something the Bush administration does not want people to see"
Michael Moore speaking about lastest film
The director has already shown the film at test screenings in the US Midwest. "The reaction was overwhelming," he said.
"People who were on the fence - undecided voters - suddenly weren't on the fence. It is certainly something the Bush administration does not want people to see."