Tsvangirai pulled out of the election because of violence in which he said nearly 90 of his followers were killed.
Monitors from both Zimbabwe's neighbours in the Southern African Development Community (SADC) and the Pan-African parliament said the vote was undermined by violence and did not reflect the will of the people.
Some of the summit leaders favour a power-sharing deal modelled on one that ended a bloody post-election crisis in Kenya this year.
Both Mugabe and Tsvangirai say they are ready for African-sponsored talks although the issue of who would lead a unity government remains a possibly insuperable obstacle.
Tsvangirai called on the summit leaders not to recognise Mugabe's re-election, after electoral officials said he won more than 85 percent of the vote, in which he was the only candidate.
"We want them (the AU) to say the 27 (June) election is illegitimate," he told Dutch public television.
Tsvangirai won the first round of elections on March 29 but fell short of the majority needed for outright victory. He said that result should be the basis for negotiating a transition.
A group of eminent international personalities, including three Nobel peace laureates, backed Tsvangirai, calling on the summit to reject the election because of the violence.
Both Tsvangirai and the group, known as the Elders, called on the AU to appoint a special envoy to mediate in the crisis.
South African Foreign Minister Nkosazana Dlamini Zuma said Zimbabwe was deeply divided and polarised after the election.
"ZANU-PF and the MDC must enter into negotiations which will lead to the formation of a transitional government that can extricate Zimbabwe from its current political challenges," a foreign ministry statement said.
It said neither ZANU-PF nor MDC were "able individually to extricate Zimbabwe from the current impasse."
Analysts believe Mugabe ignored international condemnation and went ahead with the vote so he could negotiate with Tsvangirai from a position of strength.
U.S. Secretary of State Condoleezza Rice has urged international action against Mugabe's government, including U.N.-authorised sanctions and an arms embargo.
U.N. Secretary-General Ban Ki-moon believes the election did not reflect the will of Zimbabwe's people and the result was not legitimate, his spokesman said on Monday.
State media in Zimbabwe said police had arrested 14 MDC activists, including a recently elected member of parliament, for carrying weapons and intimidating voters.
