The MDC Alliance says the ruling Zanu-PF party is attempting to rig the vote to allow President Emmerson Mnangagwa to win, and the delay in releasing official results is unacceptable.
The electoral commission has said there has been no cheating and it needed time to collate the votes.
The polls were the first since long-serving ruler Robert Mugabe was ousted.
The vote attracted a high turnout of 70% and was monitored by international observers.
Speaking at a press conference in the capital, Harare, the MDC Alliance’s Tendai Biti said there was a clear attempt by Zanu-PF to interfere “with the people’s will”.
He warned the party not to “plunge Zimbabwe into chaos”.