Protesters in Iran have demanded the government re-run June 12 election that saw an overwhelming victory for Mahmoud Ahmadinejad, the incumbent president.
At least 19 people have been killed in post-election clashes across Iran between protesters and riot police and paramilitaries.
While the broad-based protests have focused on the legitimacy of the entire presidential election, most of the demonstrators are supporters of Mir Hossein Mousavi, Ahmadinejad's main challenger in the poll.
'World watching Iran'
Obama said again that the world was watching events in Iran, and that how Tehran handles dissent from its own people "will help shape the tone not only for Iran's future but also its relationship to other countries".
Marwan Bishara, Al Jazeera's senior political analyst, said Obama needed to deplore the violence in Iran, while underlining US respect for Iran's political and territorial integrity.
"His entire discourse on Iran is based on civil and human rights - it is not about political rights," Bishara said.
"When it came to the question of the Iranian elections and their legitimacy, Obama said Iranians doubt the legitimacy of the elections; he said that he did not have observers on the ground so he could not judge on that issue."
The US president has been criticised by Republicans in the US who say he should do more to place pressure on Iran.
Rob Reynolds, Al Jazeera's senior Washington correspondent, said: "I believe criticisms [of Obama's handling of the Iran elections issue] will continue. What Obama has done here is change his rhetoric a little bit, but the policy stays exactly the same.
"His position has been exactly the same since the dispute over the election on June 12 began, which is that the United States has a strategic interest, of profound national security interests, of engaging with Iran over its nuclear programme and its support for various groups in the Middle East, such as Hamas and Hezbollah."
Obama's remarks also come amid heightened international tensions over the crisis in Iran following the country's disputed poll.
The UK said on Tuesday it was expelling two Iranian diplomats after Tehran ordered two British diplomats to leave the country.
Tehran has also accused the US and Britain of seeking to interfere in Iran's internal affairs.
|Obama criticised Iran while maintaining that the US respects its sovereignty [Reuters]
Though Ayatollah Ali Khamenei, Iran's supreme leader, has agreed to extend the deadline for filing election complaints by five days, the country's highest legislative body has refused to annul the poll results, a key demand of the Iranian opposition movement.
A spokesman for the Guardian Council said there would not be a fresh vote.
"If a major breach occurs in an election, the Guardian Council may annul the votes that come out of a particular affected ballot box, polling station, district or city," Abbas Ali Kadkhodaei was quoted as saying by Press TV, an Iranian government-funded station.
"Fortunately, in the recent presidential election we found no witness of major fraud or breach in the election. Therefore, there is no possibility of an annulment taking place," he said.
Mousavi along with Mehdi Karroubi and Mohsen Rezaei - the other two defeated presidential candidates - have rejected the veracity of the poll and demanded that fresh elections be held.