The Melancholia director joked that he could "understand" Hitler when addressing his German roots.
"I think he did some wrong things, yes absolutely, but I can see him sitting in his bunker at the end... I think I understand the man," von Trier commented.
Cannes Film Festival organisers admitted that they were "disturbed about the statements made by Lars von Trier in his press conference" and "asked him to provide an explanation for his comments".
A Cannes press release read: "The director states that he let himself be egged on by a provocation. He presents his apology.
"The direction of the Festival acknowledges this and is passing on Lars von Trier's apology. The Festival is adamant that it would never allow the event to become the forum for such pronouncements on such subjects."
Von Trier also commented through Melancholia's US distributor Magnolia Pictures, saying: "If I have hurt someone this morning by the words I said at the press conference, I sincerely apologise. I am not antisemitic or racially prejudiced in any way, nor am I a nazi (sic)."
> Melancholia review
> Lars Von Trier talks Hitler, porn and Melancholia
> Watch the Melancholia trailer video here
> Cannes Film Festival complete coverage
Watch the trailer for von Trier and Kirsten Dunst's Melancholia below: