"We agreed to have a rerun at a date to be set by" the electoral commission, party secretary and Minister of State Didymus Mutasa said at a news conference in the country's capital city of Harare.
But Tsvangirai of the Movement for Democratic Change (MDC) is claiming that his party's unofficial vote count from the March 29 presidential election gives him an absolute majority, thereby negating the need for a second round.
While official results have not been released, an independent poll by the Zimbabwean Election Support Network estimated that neither Mugabe nor Tsvangirai won an outright majority, projecting the need for a runoff.
The MDC said it was "unjustified" that the official results of the presidential election had not yet been revealed, and that it was asking the courts to order their immediate release. The suit will be heard before the Harare High Court on Saturday, according to the Associated Press.
Otto Saki, a Zimbabwean lawyer and program coordinator of Zimbabwe Lawyers for Human Rights, said, "It would be in the MDC's best interests to learn the official results of the March 29 presidential election before accepting a runoff."
Saki noted that the independent poll had a margin of error that could propel Tsvangirai as the outright winner.
Mugabe and his ZANU-PF party are facing the greatest challenge yet to his 28-year rule.
Earlier in the week, the Zimbabwe Electoral Commission declared the results of the parliamentary election, showing that the ZANU-PF party lost its majority in parliament for the first time since 1980, when Zimbabwe won its independence from Britain.
On Friday, Mutasa charged that the opposition bribed electoral officials and said his party would also challenge the results of 16 parliamentary seats.
Zimbabwe's electoral law requires a runoff to take place within 21 days after the first election.