Tsvangirai, who leads the Movement for Democratic Change (MDC), has already said that he won the presidential election outright and his party has rejected any run-off.
They say that Mugabe, who leads the Zanu-PF party, delayed the results of the presidential poll in order to rig the election and intimidate opposition supporters in preparation for a run-off.
Opposition leader wanted
On Wednesday the state-run Herald newspaper reported that police wanted to question Tendai Biti, the MDC secretary-general, for illegally declaring results of the presidential poll.
Augustine Chihuri, the police commissioner-general, was quoted in the paper's online version as saying that Biti, said to be overseas, was "urging and abetting political violence" through political rhetoric.
Biti had proclaimed on April 2 that Tsvangirai had won the election with 50.2 per cent the votes against Mugabe's 43.8 per cent.
A senior Zanu-PF party official said that the figures suggested by the electoral commission sources were credible.
"Those figures are in line with the official figures and the MDC knows that the official tally is more or less around that but they have been inflating their numbers to claim a false victory," the official said.
Another source said that Tsvangirai had in fact taken a higher proportion of the vote, between 48 per cent and 50 per cent, while another said the opposition leader had won more than 47 per cent "but less than 50" per cent.
The electoral commission is due to start a collation and verification process on Thursday.
Mugabe's chief spokesman, George Charamba, said he was not aware of the figures leaked by government sources on Wednesday.
The MDC and human-rights groups say that Zanu-PF has led a violent campaign to intimidate Zimbabweans into voting for Mugabe in a run-off.
The government has dismissed the accusations.
The presidential vote in Zimbabwe was held simultaneously with parliamentary and senate polls, amid a worsening economic crisis.
The Zanu-PF party has already lost control of the 210-seat parliament.
The country is experiencing severe food, fuel and foreign currency shortages.
Its current rate of inflation - 165,000 per cent – is the world's highest.