Millions of Iranians were said to have voted in the first few hours
There has been a huge turnout for Iran's closely-fought election as incumbent President Mahmoud Ahmadinejad seeks a second term in office.
Long queues have been reported at polling stations, and voting has been extended by at least four hours.
President Ahmadinejad, a hardliner, faces a strong challenge from reformist former PM Mir Hossein Mousavi in a campaign dominated by the economy.
Both candidates claimed victory in the first round as polls closed.
Mr Mousavi said he was the "definite winner" and alleged that there had been widespread irregularities.
But almost immedietely afterwards, President Ahmadinejad announced that he had won.
The election is being watched closely around the world for signs of a possible shift in Tehran's attitude.
US President Barack Obama said he was "excited" about what was happening in Iran, which showed change was possible.
"Ultimately the election is for the Iranians to decide," he said.
"You're seeing people looking at new possibilities. And whoever ends up winning the election in Iran, the fact that there's been a robust debate hopefully will help advance our ability to engage them in new ways."
If no candidate gets 50% in the first round, the two front-runners will face a run-off vote.
The BBC's Jon Leyne, in Tehran
There were queues snaking round the block from many polling stations. The crowds gathered outside, in segregated lines. Even as they waited to vote, they continued the spontaneous debate that's been sweeping Iran in the last week.
At one polling station, some voters came up to me, nervous that the government might be trying to defraud the election. They were worried that a bus being used as a mobile polling station was not as well monitored as the main polling centre.
But for the most part election day has continued the good humour of recent days. One Ahmadinejad supporter, a woman in the long black religious chador, made a point of shaking hands with another woman wearing the green colours of the opposition contender, Mir-Hossein Mousavi.
There has been a surge of interest recently in
Iran's presidential election,
with unprecedented live television debates between the candidates and rallies attended by thousands.
Mr Daneshjoo has said the turnout could exceed the 1997 election, in which reformist Mohammad Khatami was elected. State-run Irna TV said more than five million people cast their vote in the first four hours of voting.
The country's Supreme Leader Ayatollah Ali Khamenei and both the leading candidates voted early in the day, calling on Iranians to exercise their right to choose the country's next president.
"I recommend them to just vote based on their own views and decisions," Ayatollah Khamenei said as he voted.
"God willing, the best and the most deserving person will be elected as the head of the executive body for a four-year period."
Mr Ahmadinejad thanked the people of Iran "for their goodness, for their greatness, for their selflessness, their sacrifices, and for their forgiveness".
Mr Mousavi said simply: "God willing, with the nationwide participation of the public, we will see better and more beautiful days."
His rivals boycotted the chance to appear on TV with him, after apparently not being offered equal airtime.
The result will be watched closely outside Iran - in the US, Israel, and European capitals - for any hint of a possible shift in the country's attitude to the rest of the world, BBC diplomatic correspondent Jonathan Marcus says.
The timing of the election is also crucial, as the US push for a new policy of engagement with Tehran cannot really get going until the outcome of the election is clear, our correspondent adds.
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