ZANU-PF, Mugabe's party, is pushing for the release of the results to be delayed and votes recounted.
Tendai Uchena, the presiding judge, said: "I find that the application is urgent. The case should now proceed."
Alec Muchadehama, an MDC lawyer, told the court: "The applicants have a legitimate concern to have the results announced expeditiously. The applicants have a clear right to the results.
He told the court the vote recount sought by the ruling ZANU-PF could only happen if the results were formally announced.
"How can someone challenge results that are not known? Where did those people get the results to enable them to make these challenges?" he said.
The winner requires 50% to win outright and Tsvangirai says he has taken 50.3% of the vote.
Tsvangirai has accused Mugabe, 84, of planning violence to overturn the results of the presidential and parliamentary votes.
Long legal delays could also give Mugabe more time to organise a fightback for any runoff vote.
In another legal case complicating the election stalemate, police said at least five poll officials around the country were due to appear in court charged with undercounting votes cast for Mugabe.
ZANU-PF says that its projections show that although Tsvangirai defeated Mugabe in the presidential vote, he failed to win an absolute majority and will be forced into a runoff.
Electoral rules say this must be held three weeks after the release of results.