But the government has been quick in condemning the claim, saying the opposition should have waited for the official outcome.
Ndlovu Sikhoanyiso, the information minister, slammed the MDC for jumping the gun.
"Why rush to announce the results before the Zimbabwe Electoral Commission finishes?" he said.
"What if the final results are contrary to what they claim? Let's let the electoral commission complete its job then we can start talking from there."
Bright Matonga, the deputy information minister, also criticised the announcement.
"If the MDC thinks they have won, why don't they wait. What is urgent?" he told the BBC.
"Let it come from official sources."
George Charamba, Zanu PF presidential spokesman, told Aljazeera:
"They [the opposition] are trying to rig the elections. It’s calibrated in such a way that they just get over the half, that is required and one can see that they are anxious for the results."
"I think its both, the number has a bearing on what they are doing by way of breaking the law, to the extent that Tsvangirai was flanked by a lawyer. He surely got a good advice. There is a standard pattern for persons who break the law, the law will take its course and I can assure you that there will be reactions."
Counting of votes has progressed at a snail's pace, raising fears of rigging and fraud.
The MDC has consistently questioned the impartiality of the commission, a theoretically independent body whose leadership was appointed by Mugabe.
The commission has been under growing pressure, including from foreign governments to declare the official results, with the opposition charging that the hold-up is designed to buy time for Mugabe to fix the outcome.
The commission has said the hold-up is down to the complex nature of the polls, the first time that the contest for president and parliament has been held at the same time.
Mugabe, who has ruled the former British colony since independence in 1980, said before the election that his old rival Tsvangirai would never rule the country in his lifetime.