Iran's electoral authorities say they have found no evidence of fraud in the presidential election.
Few thought Mahmoud Ahmadinejad would sweep into second place
The country's Guardians Council, which ran the poll, said a partial recount had confirmed the result and a run-off vote would go ahead Friday.
One hundred ballot boxes in four cities were randomly selected for the recount after complaints of dirty tricks.
Tehran Mayor Mahmoud Ahmadinejad faces former President Akbar Hashemi Rafsanjani in the run-off.
"After complaints... the Guardians Council authorised the interior ministry to recount the ballots from a certain number of boxes. It was clear there was no fraud," the head of the Guardians Council, Ahmad Jannati, said in a statement read on state television.
"The vote was sound and the second round will be held on Friday."
Some 40 ballot boxes in Tehran and 20 from each of the other cities were recounted.
This is a tiny fraction of the overall total number of ballot boxes, and does not include remote rural areas where fraud might be easier, says the BBC's Frances Harrison in Tehran.
Candidate Mostafa Moin, who came fifth, and a number of other reformists accused the Guardian Council of carrying out a multi-million dollar campaign to mobilise 300,000 Islamic militias to ensure a hardliner's success.
They complained of a number of irregularities that they said were aimed at propelling Mr Ahmadinejad into the run-off with the more moderate Mr Rafsanjani.
Akbar Hashemi Rafsanjani - 21%
Mahmoud Ahmadinejad - 19.5%
Mehdi Karroubi - 17.3%
Source: Iranian interior ministry
"Take seriously the danger of fascism," Mr Moin said. "Such creeping and complex attempts will eventually lead to militarism, authoritarianism as well as social and political suffocation in the country."
Two newspapers were closed down overnight by Iran's hardline judiciary for planning to print a letter of complaint by another reformist candidate Mehdi Karroubi, who narrowly lost out to Mr Ahmadinejad.
Such persistent allegations of vote-rigging are unprecedented since the revolution and the closure of newspapers is a clear warning to local media not to touch the story, says our correspondent.
Iran's reformist leaders have urged supporters to rally behind Mr Rafsanjani, who also spoke out over what he called a "tarnished" poll.
"The Islamic revolution is at a difficult crossroads, facing domestic and foreign threats and adventurism," he said.
Traditionalist conservatives have been urged to put their full weight behind Mr Ahmadinejad.
No Iranian presidential election has gone to a second round before.