Tsvangirai, during a news conference, called Wednesday's polling a "huge farce" and declared it "null and void" as an observer group said up to a million people were barred from casting ballots, the BBC reported Thursday.
Mugabe's Zanu-PF party, which has begun claiming victory, denied the accusations and said voting went smoothly.
The head of the African Union observer mission, former Nigerian President Olusegun Obasanjo, said his initial assessment indicated the vote was free and fair. Other regional observers also praised the peaceful nature of the election, the first presidential balloting held in Zimbabwe since 2008 when violence erupted.
The Zimbabwe Electoral Commission has five days to declare a winner.
Speaking at the Movement for Democratic Change headquarters in Harare, Tsvangirai said, "Our conclusion is that this has been a huge farce. The credibility of this election has been marred by administrative and legal violations which affected the legitimacy of its outcome."
"It's a sham election that does not reflect the will of the people," he said.
Monitors from the Zimbabwe Election Support Network earlier said the poll was "seriously compromised."
In a statement, the network said potential voters were turned away from 82 percent of polling stations in urban areas, where support for Tsvangirai is strong. The percentage of voters denied ballot access in areas considered Mugabe strongholds was lower.
Zanu-PF spokesman Psychology Maziwisa denied many voters were deliberately barred from registering. He admitted to some irregularities, stressing the two main parties were both 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," Maziwisa told the BBC.
"If you look at the Zimbabwean situation you can only come to one conclusion," Maziwisa said. "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."
Mugabe, 89, pledged to step down after more than three decades in power if he loses to Tsvangirai.
Mugabe and Tsvangirai have shared governance since 2009 through an agreement brokered to end the deadly violence that broke out following a disputed presidential election in 2008.
A presidential candidate must garner more than 50 percent of the vote to be declared the winner. If no candidate reaches that threshold, a runoff will be held Sept. 11.