Zimbabweans should be able to "enjoy genuine freedom" so they can "choose their leaders out of their own will without being intimidated", Ban told a news conference in Tokyo on Tuesday
"You have my full commitment that I will spare no efforts to work out a solution," he said.
On Monday African leaders refrained from criticising Mugabe, despite Western demands they take a tough stance over his re-election.
But behind the scenes, some leaders are said to be pushing for Mugabe to share power with Morgan Tsvangirai, the leader of the opposition Movement for Democratic Change (MDC).
However, a Mugabe spokesman dismissed calls for a Kenya-style grand coalition government, saying the crisis in the country would be decided the "Zimbabwean way".
|Morgan Tsvangirai says Mugabe's re-election is a sham [AFP]
George Charamba told journalists at the AU summit: "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 way. Not at all."
Amr el-Kahky, Al Jazeera’s correspondent reporting from Sharm el-Sheikh, said leaders of the regional Southern African Development Community (SADC) met on Monday night.
"We understand that there were some recommendations that are due to be passed to the leadership of the AU today," he said.
"We don't know what these recomendations are….some people say they will recognise Mugabe, some others say they will condemn him.”
Mugabe was declared winner of a run-off election on Friday after Tsvangirai withdrew because of violence in the run up to the vote.
Many African countries, including regional power South Africa, have been unwilling to condemn Mugabe but there has been mounting criticism from the US and Europe.
During public speeches most AU leaders did not criticise Mugabe but spoke of the "challenges" in Zimbabwe and focused on other issues facing Africa.
"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.
But Jendayi Frazer, the US secretary of state for African affairs, said she believed that, in private, leaders at the summit would "have very, very strong words for him".
"I would suggest that one not take from the soft words in an open plenary
as a reflection of the deep concern of leaders here of the situation in Zimbabwe," she told reporters.
A White House spokesperson also suggested that Mugabe is facing pressure from behind the scenes.
Dana Perino said Mugabe's actions have "cast a negative light on some really good, democratic leaders in Africa.".
"There are a lot of them who are working very hard to institute democratic reforms in their own way," she said.
But some African leaders have been openly critical of Mugabe’s presence at the AU talks.
Speaking in Nairobi, Raila Odinga, the Kenyan prime minister, said Zimbabwe should be suspended from the African Union.
"They should suspend him and send peace forces to Zimbabwe to ensure free
and fair elections,'' Odinga said.
Cheikh Tidiane Gadio, Senegal's foreign minister, complained of the hesitancy to openly pressure Mugabe.
"We don't want to talk about it. That doesn't make any sense," he said.
Observers from the AU said on Monday that the Zimbabwe run-off fell short of the union’s own standards.
Many Zimbabweans complained they were forced to vote by threats of violence or arson from Mugabe supporters.