Morgan Tsvangirai, the MDC leader, told reporters in Harare, the capital, that the MDC should be recognised as the "legitimate government" of Zimbabwe.
Mugabe was sworn in for a new five-year term on Sunday after the electoral commission announced he had won about 85 per cent of the vote in the run-off, which was condemned by many as violent and unfair.
Tsvangirai defeated Mugabe in the presidential vote on March 29 but failed to win an absolute majority.
African leaders at an AU summit in the Egyptian seaside resort of Sharm El-Sheikh on Tuesday urged Mugabe and Tsvangirai to begin negotiations to end the crisis over Mugabe's re-election.
"The AU resolution is in conformity to what Mugabe said at his inauguration, when he said we are prepared to talk in order to resolve our problems," Sikhanyiso Ndlovu, the information minister, told Reuters news agency.
"We are committed to talk, not just with Tsvangirai but to other parties as well."
Unity government rejected
Tsvangirai has rejected forming a government of national unity with Mugabe, saying it would not solve the country's crisis.
"A government of national unity does not address the problems facing Zimbabwe or acknowledge the will of the Zimbabwean people," he said.
He also said that the AU had failed to acknowledge that he won the first round of Zimbabwe's election before Mugabe staged a one-man run-off last Friday.
"The resolution [put forward in Egypt] does not recognise the illegitimacy of the June 27 election and the fact that most African leaders refused to recognise Mugabe as head of state," he said.
"The resolution endorses the concept of a government of national unity without acknowledging that the MDC, as the winner of the last credible election, on March 29 should be recognised as the legitimate government of Zimbabwe."
Tsvangirai said his party was committed to negotiations on the country's crisis but these should be on the basis of finding a transitional agreement that would lead to a new constitution and fresh elections.
"While the MDC remains committed to negotiations this must be based on the March 29 result and must move towards a transitional agreement," he said.
"Our commitment to a negotiated settlement is not about power-sharing or power deals but about democracy, freedom and justice."
Tsvangirai also reiterated MDC calls for an AU mediator to be appointed, insisting that the region's chief negotiatior - Thabo Mbeki, the South African presdident - was biased towards Mugabe.
"We need an expanded mediation team which includes a representative from the AU," he said.
"It is our position that unless the mediation is expanded to include at least one permanent representative from the AU and the mediation mechanism is changed, no meaningful progress can be made towards resolving the Zimbabwean crisis.
"We have said that Mbeki ... you have taken all these years and we are not happy with you. What we want is to get another AU partner to come here and solve this problem."