Mugabe's loyalist army and police set up security posts in Harare yesterday, apparently in case there were any protest demonstrations.
"We are rejecting the results because they are fraudulent," Mr Tsvangirai said. "We will go back to our people. Our people are the ones hurting. Our people are disciplined. We don't want a violent resolution to this crisis."
He said a complete audit was needed of the shambolic lists of registered voters, which were made available to the parties only at the time of the election.
US secretary of state John Kerry said the election process was "deeply flawed" because of irregularities in the voters' roll, unequal access of the parties to state media, a lack of political reforms as mandated by the constitution, and other problems. He cited "the balance of evidence," although the United States was barred from monitoring the vote.
"The people of Zimbabwe should be commended for rejecting violence and showing their commitment to the democratic process," Mr Kerry said yesterday.
"But make no mistake: in light of substantial electoral irregularities reported by domestic and regional observers, the United States does not believe that the results announced today represent a credible expression of the will of the Zimbabwean people."
British Foreign Secretary William Hague expressed "deep concern" over the election, saying the failure to share the voters' roll with political parties was a "critical flaw". Mr Hague said that and other irregularities "call into serious question the credibility of the election".
"We note that some political parties have rejected the result on the basis of these irregularities," he said, without saying whether Britain endorsed their move. "We will need to examine what has happened and consider further reports from regional and local observer missions. In the meantime, it is important that all allegations of electoral violations are thoroughly investigated."
Mr Tsvangirai's party lost several seats in its Harare urban strongholds by massive margins compared to their overwhelming victories in 2008.
In one Harare constituency, Mr Tsvangirai's party won with 9,538 votes to 8,190 captured by Mugabe's party. In 2008, the same district voted for the MDC candidate, Tendai Biti, by about 8,300 ballots against Mugabe's 2,500 votes.
Independent monitors have charged that as many as 750,000 voters were prevented from casting their ballots on Wednesday because of irregularities in voters' lists. They also allege that thousands of unregistered voters were allowed to vote.
The continent-wide African Union and regional monitors of the Southern African Development Community, or SADC, have generally endorsed the elections as peaceful. But they have expressed misgivings over how voting numbers might have been manipulated and have demanded a full account of voter numbers from the official state election body before passing their final judgment on whether the polls were free, fair and credible.