At a news conference, Morgan Tsvangirai said that Wednesday’s poll was “null and void”.
The largest observer group earlier said up to a million people were prevented from voting.
Robert Mugabe’s party – which is claiming a victory – denied the accusations, saying the voting went smoothly.
It is illegal to publish unofficial results.
Vote counting started overnight, and the Zimbabwe Electoral Commission (ZEC) has five days to declare who won the poll.
Police have warned they would take action against anyone trying to leak early results. Extra units – some in riot gear – have now been deployed in the capital, Harare.
African regional observers have praised the peaceful nature of the election.
Speaking at his Movement for Democratic Change (MDC) headquarters in Harare, Morgan Tsvangirai said: “In our view, that election is null and void.”
“It’s a sham election that does not reflect the will of the people.”
Morgan Tsvangirai spoke shortly after the monitors from the Zimbabwe Election Support Network (ZESN) said the poll was “seriously compromised”.
In a statement, the ZESN said that potential voters were turned away from 82% of polling stations in urban areas, where support for Morgan Tsvangirai is strong.
In rural areas – seen as strongholds of President Robert Mugabe – the percentage was less than half that, the group added.
On Wednesday, villagers, MDC polling agents and the ZESN said there had been voting irregularities in rural parts of Masvingo province.
They said local traditional leaders and village heads had lined up people, forcibly marched them to the polling stations and given them voting numbers as if to cross-check who they had voted for.
They also allege that in these areas some literate people were forced to pretend they could not read or write and were assisted to cast their vote in favor of Zanu-PF.
Zanu-PF spokesman Psychology Maziwisa denied that many voters had been deliberately prevented from registering.
He admitted that there were some irregularities, but stressed that both main parties had been affected.
“You’ve got to bear in mind that that was partly due to the fact that resources were not being made available by the finance minister who is Tendai Biti, who comes from the Movement for Democratic Change party,” he said.
“If you look at the Zimbabwean situation you can only come to one conclusion. And that is that over the last four years we’ve made a lot of effort to make this environment in Zimbabwe as conducive as it possibly can [be] for an election that is free and fair.”
Robert Mugabe, 89, has pledged to step down after 33 years in power if he and his party lost.
President Mugabe’s Zanu-PF party and Morgan Tsvangirai’s MDC have shared an uneasy coalition government since 2009 under a deal brokered to end the deadly violence that erupted after a disputed presidential poll the previous year.
The first round of the 2008 poll was also praised for being peaceful – trouble broke out after the results were announced, with Morgan Tsvangirai gaining more votes than Robert Mugabe.
On Tuesday, the MDC accused Zanu-PF of doctoring the roll of registered voters, which was released by the ZEC only on the eve of the polls after weeks of delay.
The MDC claimed the roll dated back to 1985 and was full of anomalies.
It appears the document features the names of thousands of dead people.
MDC Secretary-General Tendai Biti said there were as many as two million such names, while some genuine voters were not on the rolls.
The MDC has already handed its evidence to observers from the Southern African Development Community (SADC).
But a senior Zanu-PF member has denied the allegations, saying that appointees from both parties were in the electoral commission.
In addition to Robert Mugabe and Morgan Tsvangirai, there are three other candidates standing for the presidency: Welshman Ncube, leader of the breakaway MDC-Mutambara; Dumiso Dabengwa of the Zimbabwe African People’s Union (Zapu), and Kisinoti Munodei Mukwazhe, who represents the small Zimbabwe Development Party (ZDP).
To be declared a winner, a presidential candidate must win more than 50% of the vote. If no candidate reaches this mark, a run-off will be held on September 11.
The elections were the first to be held under the new constitution approved in a referendum in March this year.
On Wednesday, voters were also electing the country’s new parliament.
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