Tsvangirai said that Mugabe was creating a political crisis in the southern African country, and that an election could be held no earlier than August 25.
Addresing a news conference on Thursday, the PM said that Mugabe had violated a power-sharing agreement, set up after bloody and disputed polls five years ago, under which he has been a partner in a factious unity government.
"Mugabe is deliberately precipitating a constitutional crisis," Tsvangirai told a news conference. "As prime minister I cannot and will not accept this."He reiterated his view that the state media and security forces needed to be reformed before any poll to ensure it was fair.
Earlier in the day, President Mugabe has unilaterally declared elections would be held on July 31, by-passing parliament in a bid to comply with a constitutional court order to hold elections by July 31.
Mugabe, 89, has been Zimbabwean leader for 33 years, serving first as prime minister and later as president.
A day before Mugabe's announcement, Tsvangirai said he would not give legitimacy to the elections.
"You can't set a date of an election without my concurrence. Period. I will not give legitimacy to that election date unless we agree," Tsvangirai told civil society organisations in the capital Harare.
Zimbabwe is due to elect a successor to Mugabe's four-year power-sharing government with Tsvangirai, who heads the opposition Movement for Democratic Change (MDC).
The tenure of the power-sharing government, which was formed in 2009, ends on June 29.
Earlier this month the Constitutional Court ordered that the elections be held by the end of July.
Tsvangirai, however, has pushed for for a later vote, pending reforms aimed at ensuring the elections will be free and fair.
Regional mediators who brokered the initial power-sharing government in 2008 will meet on Saturday to discuss the new polls' organisation and funding, said Tsvangirai.
Tsvangirai won the first round of the last election in 2008 but failed to gain a clear majority to form a government.
He boycotted the second round of the vote - won by Mugabe - amid a surge in attacks and intimidation against his supporters.