The AU also resolved "to support the call for the creation of a government of national unity," the official said.
However, Botswana called on Tuesday for Zimbabwe to be suspended from meetings of the AU and Southern African Development Community (SADC) due to Mugabe's controversial re-election.
Zimbabwe's feuding political parties had earlier rejected any prospect of a negotiated settlement to the country's political crisis.
"Kenya is Kenya. Zimbabwe is Zimbabwe. We have our own history of evolving dialogue and resolving political impasses the Zimbabwean way. The Zimbabwean way, not the Kenyan"
George Charamba, spokesman for Robert Mugabe
The MDC said that the re-election of Robert Mugabe as Zimbabwe's president had ended any chance of a unity government.
"While the MDC has pursued dialogue in a bid to establish a government of national healing before June 4, the sham election on June 27, 2008, totally and completely exterminated any prospect of a negotiated settlement," Tendai Biti, deputy leader of the MDC, said on Tuesday.
The MDC statement came shortly after George Charamba, a spokesman for Mugabe, dismissed calls for a Kenya-style grand coalition government.
"Kenya is Kenya. Zimbabwe is Zimbabwe. We have our own history of evolving dialogue and resolving political impasses the Zimbabwean way," Charamba said at the AU summit.
"The Zimbabwean way, not the Kenyan way. Not at all."
The AU resolution comes a day after most political leaders at the summit refrained from criticising Mugabe, despite Western demands they take a tough stance over his re-election.
|Morgan Tsvangirai says Mugabe's
re-election is a "sham" [AFP]
Ban Ki-moon, the UN secretary-general, pledged to work to resolve the political crisis in Zimbabwe and repeated his view that Mugabe's re-election lacked legitimacy.
Zimbabweans should be able to "enjoy genuine freedom" so they can "choose their leaders out of their own will without being intimidated", Ban said in Tokyo on Tuesday.
"You have my full commitment that I will spare no efforts to work out a solution," he said.
Many African countries, including regional power South Africa, have been unwilling to condemn Mugabe's re-election but there has been mounting criticism from the US and Europe.
But the US has prepared UN sanctions in response to Mugabe's re-election.
James McGee, the US ambassador to Zimbabwe, told Al Jazeera that African nations had to focus on Zimbabwe in the aftermath of the disputed election.
"No matter what type of statement comes out of the African Union we still believe that the diplomatic process must be a robust one. We have to work with the diplomatic community across Africa to ensure that the diplomatic light stays on Zimbabwe.
"[Mugabe’s government] cannot hide in the dark and continue its nefarious practices. We want the world to see what is happening in Zimbabwe."
European governments are also considering fresh sanctions on Zimbabwe, France’s foreign ministry spokesman said as Paris assumed the rotating EU presidency on Tuesday.
The new measures, which follow sanctions in 2007, could include imposing visa bans and asset freezes on Mugabe's closest loyalists, Eric Chevallier said.