The MDC claims the Zanu-PF has waged a campaign of violence against it while the ruling party prepares for a second round presidential run-off.
The opposition has ruled out Tsvangirai's participation in any run-off, saying a second ballot would be undemocratic due to Mugabe's intimidation tactics.
The state media quoted George Chiweshe, the electoral commission chairman, as saying that ballots would be counted again in the presence of party representatives, candidates and election observers next Saturday.
Nelson Chamisa, an MDC spokesman, said the recount was "designed to reverse the will of the people".
Call for results
Meanwhile, southern African leaders called on Zimbabwe's election commission to publish the results of the March 29 presidential election as soon as possible.
The call came after a 13-hour meeting of the Southern African Development Commission (SADC) in Zambia, which had been specially convened to discuss the political deadlock.
"The summit urged the electoral authorities in Zimbabwe that verification and release of results are expeditiously done in accordance with the due process of law," a joint statement from 14 nations said on Sunday.
"[The] summit also urged all the parties in the electoral process in Zimbabwe to accept the results when they are announced."
Tendai Biti, the MDC secretary-general, said his party was largely satisfied with the outcome of the Zambia summit.
"This is a major improvement, SADC has acquitted itself fairly well," he said.
However, Biti urged Thabo Mbeki, South Africa's president, to end his policy of so-called quiet diplomacy in mediating in Zimbabwe.
Mbeki must show "more vigour, more openness and a complete abandonment of the policy of quiet diplomacy", he said.
SADC on Sunday called on Mbeki to continue as chief mediator between the MDC and the ruling Zanu-PF.
Mugabe did not attend the summit, after initially saying he would do so.
Tsvangirai addressed the leaders and asked them to urge Mugabe to quit, but the Zimbabwean leader was not even mentioned in the four-page statement from the 14 leaders.
Mugabe's allies had suggested that Saturday's summit was part of a Western plot to overthrow him because of his land reform programme, which took white-owned farms and redistributed them to blacks.
"This time, African leaders are supposed to do the bidding of the white West, that is to pressure Zimbabwe to abet regime change agenda," a column in the Herald newspaper said.