But he also said the world was inspired by the Iranian demonstrators who took to the streets in protest after Mahmoud Ahmadinejad, the incumbent president, was officially declared the winner in his re-election bid.
The US leader also vowed to continue direct diplomacy with Tehran over its nuclear programme.
The comments are the first by Obama since disputed election results set off widespread protests across Iran.
Al Jazeera's Rob Reynolds in Washington said the crisis was the biggest foreign policy faced by Obama since he took office in January.
The US government's comments came after Joe Biden, the US vice-president, said on Sunday that he had "doubts" about the validity of the election.
"It sure looks like the way they're suppressing speech, the way they're suppressing crowds, the way in which people are being treated, that there's some real doubt," Biden told NBC television channel.
Official election results gave Ahmadinejad nearly 63 per cent of the vote, with Mousavi only garnering 34 per cent.
"That's what they're announcing. We have to accept that for the time being. But there's an awful lot of question about how this election was run," Biden said.
Biden said the US was going wait for "a thorough review" of the whole process before reacting further.
Hillary Clinton, the US secretary of state, said she hoped the outcome reflected the "genuine will and desire" of Iranian voters.
Clinton was responding to allegations by supporters of Mousavi that the outcome was rigged to give Ahmadinejad a decisive victory.
Gordon Brown, the UK prime minister, said on Monday that the way the Iranian government responded to the protests would "have implications for Iran's relationships with the rest of the world in the future".
"The [Iranian] regime must address the serious questions which have been asked about the conduct of the Iranian elections," he told the British parliament.
Germany and France summoned Iran's ambassadors to express concern over the use of force by police against demonstrators.
"The actions of the Iranian security forces are completely unacceptable," Frank-Walter Steinmeier, the German foreign minister, said on public television.
After a meeting in Luxembourg, EU foreign ministers expressed "serious concern" at the weekend crackdown and called for an inquiry into the conduct of the election.
Ban Ki-moon, the UN secretary-general, said he had noted that Ayatollah Ali Khamenei, Iran's supreme leader, had ordered officials to look into the fraud allegations.
"I am closely following how this investigation will come out," he said, reiterating that "the genuine will of the Iranian people should be reflected and respected in the most transparent, fair and objective manner".