Zanu-PF lost in 21 of the 23 constituencies due to be examined and hopes that a new count will enable it to retake control of the 210-seat assembly.
"We, as a party, will not accept any recount in respect of parliamentary seats," Tendai Biti, MDC secretary-general, said.
"We have no doubt on the insistence of a recount because ballot boxes have been stuffed. Those ballot boxes have become pregnant and reproduced."
The MDC regards Zimbabwe's electoral commission, whose leadership is appointed by the government, as a partisan body despite its nominal independent status.
Tsvangirai has already announced himself the victor over Mugabe in the presidential vote, saying that he won a majority on March 29.
But Zanu-PF says that neither Mugabe nor Tsvangirai won over 50 per cent of the vote needed to win the presidency.
The party has declared that there will be a run-off presidential election with Mugabe as its candidate.
Mugabe, 84, did not mention the election outcome or whether he would stand in a run-off during celebrations on Friday to mark Zimbabwe's 28th anniversary of independence from Britain.
He instead criticised London, saying it had bribed voters to mark their ballots for the MDC.
"Through money as a weapon, [the British] literally buy some of our people to turn against their government, and accept to be politically manipulated in abandoning their rights," Mugabe said.
Tsvangirai has alleged that Zanu-PF is preparing for a "war" against the people, referring to a shipment of weapons aboard a Chinese ship that arrived in the port of Durban destined for Zimbabwe.
A South African high court judge on Friday refused permission for the weapons to be transported across the country to Zimbabwe.
The ship later left the port for an unknown destination, SAPA news agency reported.