Sony Pictures says it is looking at different ways to release the film satire the Interview, after scrapping its opening following a cyber-attack blamed on North Korea. It said it had only cancelled the film's Christmas Day release after cinemas pulled out. The company said it was "surveying alternatives to enable us to release the movie on a different platform".
"We cannot have a society in which some dictator someplace can start imposing censorship in the United States," he said.
He also vowed to "respond" to the cyber-attack in a "manner that we choose".
The FBI has said that North Korea was responsible for the hack, but Pyongyang denies this. The Interview depicts the assassination of North Korean leader Kim Jong-un.
Responding to the president's comments, Sony Pictures chief executive and chairman Michael Lynton told CNN it had not made an error in pulling the film. (The president said Sony made a mistake in not releasing its film)
"We have not caved, we have not given in, we have persevered and we have not backed down," he said.
A Sony statement said the decision not to go ahead with the Christmas Day release was based on "the majority of the nation's theatre owners choosing not to screen the film".
"Let us be clear - the only decision that we have made with respect to release of the film was not to release it on Christmas Day in theatres, after the theatre owners declined to show it," the statement added.
"Without theatres, we could not release it in the theatres on Christmas Day. We had no choice.
"It is still our hope that anyone who wants to see this movie will get the opportunity to do so."
Script details, salary data and private email correspondence were leaked in the wake of November's huge cyber attack.
Hackers then issued a warning referring to the 11 September 2001 terror attacks, saying "the world will be full of fear" if The Interview was screened.
North Korea earlier this month denied involvement in the hack - but praised the attack itself as a "righteous deed". An article in the state-run KCNA news agency, quoting the country's top military body, said suggestions that Pyongyang was behind the attack were "wild rumour".
The movie features James Franco and Seth Rogen as two journalists who are granted an audience with Mr Kim. The CIA then enlists the pair to assassinate him.
The film's cancelled release drew criticism in Hollywood, with some calling it an attack on the freedom of expression. Actor George Clooney told the trade website Deadline on Thursday the film should be released online, saying Hollywood should not be threatened by North Korea. Mr Clooney has a good point and so does Mr Obama. If we allow cyber bullying to win this time, it opens a Pandora's box of cyber terrorist attacks by N Korea and any other pissed off hostile country. And it clearly goes to the heart of one of America's most inviolable rights...freedom of speech.