Meanwhile, Iran's President Mahmoud Ahmadinejad arrived in Russia on Tuesday to attend a regional summit - a trip that had been delayed due to the protests.
In his first public comments on the situation in Iran, Mr Obama said: "I am deeply troubled by the violence that I've been seeing on television.
"I think that the democratic process, free speech, the ability for folks to peacefully dissent, all those are universal values and need to be respected."
But the BBC's Jonathan Beale, in Washington, says the president studiously avoided any comment on the allegations of vote fraud.
"We respect Iranian sovereignty and want to avoid the United States being the issue inside of Iran," Mr Obama said.
Earlier on Monday, hundreds of thousands of people, some shouting "death to the dictator", marched through the streets of Tehran to protest against the re-election of Mr Ahmadinejad.
AT THE SCENE
Jon Leyne Reporting from Tehran
It was an incredible sight. A huge crowd, hundreds of thousands of people maybe even millions of people there in defiance of open threats from the government that they should not assemble.
The security forces were staying well away - we were even able to film and usually the secret police come in straight away and stop you.
But the crowds were so enormous they were stepping back.
Iran's conservative-dominated Guardian Council is considering complaints filed by Mir Hossein Mousavi and fellow defeated candidate Mohsen Rezai, alleging that the poll was rigged.
The BBC's Jon Leyne, in Tehran, says the rally was the biggest demonstration in the Islamic republic's 30-year history and described it as a "political earthquake".
The government had outlawed any protest following two days of unrest, with the interior ministry warning that "any disrupter of public security would be dealt with according to the law".
Despite this, correspondents said riot police had been watching the rally during the afternoon and had seemed to be taking no action.
The first indications of trouble came at about 2045 local time (1615 GMT), when protesters were beginning to disperse from Tehran's Azadi (Freedom) Square.
An Iranian photographer told AFP news agency that the shooting happened outside a base of the Basij volunteer militia, which was set on fire. The dead man had been shot in the head.
Fire on the streets of Tehran as mass protests continue
Pictures of the incident showed armed men, in civilian clothes but wearing helmets, pointing guns at the crowds from the roof of the base. The photographer said the protester had been killed by shots fired by the armed men.
Other sources told the BBC as many as six people might have died in the incident.
A BBC correspondent said there had also been gunfire in the north of the city - traditionally an anti-government stronghold - and that the security forces appeared to be hunting down protesters.
There was a large police presence on major streets of the city on Monday night, but evidence of few ordinary people, our correspondent added.
Earlier, the demonstrators had gathered in Tehran's Enghelab (Revolution) Square, chanting pro-Mousavi slogans.
"Mousavi we support you. We will die, but retrieve our votes," they shouted, many wearing the green of Mousavi's election campaign.
More than 100 opposition figures arrested, including the brother of ex-reformist President Khatami
Local and international phone and text message services interrupted
Social networking and newspaper websites blocked
"Heavy electronic jamming" from inside Iran disrupts BBC Persian TV service
International journalists arrested and asked to leave
Iranian newspapers do not carry reports of the violence
Mr Mousavi eventually appeared, addressing the crowd from the roof of his car.
"The vote of the people is more important than Mousavi or any other person," he told his supporters.
Elsewhere in Iran, pro-Mousavi demonstrators were reported to have clashed with police in the historic city of Esfahan and the north-eastern city of Mashhad.
Police in Shiraz, south-west Iran, fired into the air to disperse demonstrations, witnesses said.
A crowd of about 2,000 people also took to the streets in the heavily Arab city of Ahvaz near the Iraqi border, reports say.
Mr Mousavi has said that another rally is planned for Tuesday in north Tehran.
The 12-member Guardian Council is due to meet Mr Mousavi and Mr Rezai on Tuesday to discuss their grievances.
State television reported that Supreme Leader Ayatollah Ali Khamenei, who has upheld the election result, urged the Guardian Council to "precisely consider" the complaints.
But the Iranian leadership has put itself in an impossible position, our Tehran correspondent says.
He says that Ayatollah Khamenei has given his complete endorsement to the election result and to Mr Ahmadinejad, and by doing so he has put at risk the very foundations of the Islamic republic.
Dozens of opposition activists have been arrested since the protests began, while internet sites appear to have been blocked and the media heavily restricted.
UN Secretary-General Ban Ki-moon said he was following the situation closely.
"The position of me and the United Nations is that the genuine will of the Iranian people should be fully respected," he told reporters.
EU foreign ministers expressed "serious concern" and called for an inquiry into the conduct of the election, while France and Germany each summoned their Iranian ambassadors to explain what was going on.
German Chancellor Angela Merkel criticised the use of "completely unacceptable" force against protesters and called for a "transparent evaluation of the election result".
While the result of the election is disputed, correspondents note that Mr Ahmadinejad does have the backing of millions of Iranians.
Groups of his supporters gathered outside French and British embassies in Tehran on Monday, protesting against what they consider to be foreign interference in Iran's affairs.
"We have gathered here to protest the hidden interference of the Brits and the world, who are trying to create chaos in our country," one protester said.
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