His political opposition also took a hard line on power-sharing, further reducing prospects of a quick resolution after last weekend's run-off election in which Mugabe was the sole candidate.
Leaders at the Egyptian AU summit, in its second and final day, were unwilling to publicly criticise Mugabe and instead gently pushed behind the scenes that he accept some sort of power-sharing agreement.
But Mugabe's spokesman George Charamba dismissed prospects of sharing power and said that the 84-year-old would not step down.
"He's a few days into office and you expect him to retire, do you? ... Five days have expired, not even a week after. ... Why is the issue of the retirement of the president of Zimbabwe such an obsession for the West?" he said.
"He has come here as president of Zimbabwe and he will go home as president of Zimbabwe, and when you visit Zimbabwe he will be there as the president of all the people of Zimbabwe," he said.
The United Nations has "made it clear" that dialogue between Mugabe and his rival Morgan Tsvangirai is necessary, UN Deputy Secretary-General Asha-Rose Migiro said.
"It is the hope of the UN that the African Union and African leaders will get their act together to address this issue," she said.
The United States, Britain and other European countries have widely condemned Zimbabwe's run-off. The US is pushing for more financial and travel sanctions against Mugabe supporters and is urging the UN Security Council to impose an arms embargo.
Prime Minister Gordon Brown has urged the African Union to reject the result of the run-off, and France says it considers Mugabe's government "illegitimate."
Charamba had harsh words for Western pressure: "They can go hang. They can go and hang a thousand times."
He also demanded that Zimbabwe be left to determine its own future.
"The way out is the way defined by the Zimbabwe people free from outside interference, and that is exactly what will resolve the matter," he said.
In Zimbabwe, there also were strong doubts about an agreement, even as Mr Tsvangirai left the Dutch Embassy, where he had fled for safety after announcing his withdrawal from the run-off because of state-sponsored violence against his supporters.
Tendai Biti, no. 2 in Mr Tsvangirai's Movement for Democratic Change party, dismissed speculation that his party and Mugabe's ZANU-PF were about to conclude an agreement to govern together.
"Nothing can be as malicious and as further from the truth," he said. "As a matter of fact, there are no talks or discussions taking place between the two parties and most importantly, there is no agreement in the offing."
During public speeches at the summit's opening yesterday, most AU leaders spoke of the "challenges" Zimbabwe was facing and none said anything harsh about Mugabe.
But Jendayi Frazer, the assistant US secretary of state for African affairs, said she believed that in private, the leaders were going to "have very, very strong words for him."
Key African leaders have long had close ties to Mugabe, renowned as a campaigner against white rule and colonialism and Zimbabwe's ruler since its independence in 1980. They are also reluctant to be seen as backing the West, former colonial rulers, against a fellow African.
Meanwhile Sir John Holmes the UN undersecretary-general for humanitarian affairs, said he was very concerned for up to four million Zimbabweans who have become increasingly dependent on food aid.
"We expect a poor harvest again in Zimbabwe," Sir John said, referring to the crop of winter wheat due in the coming months.
Zimbabwe's main harvest in April was already at a record low mainly because of lack of rain, untimely delivery of seeds and a shortage of fertiliser.
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