The 84-year-old stood unopposed after Morgan Tsvangirai, the leader of the main faction of the MDC, withdrew from the campaign alleging violence, voter intimidation and the displacement of hundreds of people.
George Sibotshiwe, Tsvangirai's spokesman, told Al Jazeera that the talks were taking place but his party had refused to take part.
"We were invited, but we refused to take part. We do not recognise Mugabe," he said from Johannesburg in South Africa.
"We cannot take part in talks with Mbeki on his own as they are contrary to the resolution of the AU. The AU must appoint an envoy to mediate. Mbeki is trying to create an idea as mediator just before he goes to the G8."
In brief comments to reporters after the meeting, Mbeki said that he hoped to meet Tsvangirai at a later stage.
"It was the view of the facilitators and the Zimbabwean leadership that we need to move with some speed," he said.
"We agreed that MDC-Tsvangirai has to be part of the negotiations so we are hoping that the process will take place with them."
An African Union summit in Egypt attended by Mugabe last weekend ended with a call for all parties to hold talks on forming a national unity government.
|Tsvangirai declined to attend the meeting and refuses to accept Mugabe's re-election [AFP]
Al Jazeera's Haru Mutasa, reporting from Harare, said that the two sides that attended the meeting had agreed to hold more talks at a future date.
"They are now urging Morgan Tsvangirai's faction to come to the table," she said.
"The big question that is being asked is how far can these talks go without Morgan Tsvangirai."
Patrick Chinamasa, Zimbabwe's justice minister, said Tsvangirai had shown a lack of respect by staying away from the talks.
"We are committed to dialogue with all the two MDC formations," he said. "But it was utter disrespect for Morgan Tsvangirai to agree last night ... to meet the facilitator here and it is an act of utter disrespect for him not to have turned up."
Mutambara, who has had a difficult relationship with Tsvangirai, also criticised the MDC leader.
"For these negotiations, for this political settlement to make sense, all political parties must be involved," he said.
Mugabe told thousands of supporters on his return from the summit that Tsvangirai should not "delude" himself into thinking the election result could be removed from the record books and should renounce his claims to the presidency.
"I am the president of the republic of Zimbabwe and that is the reality," he said.
"Everybody has to accept that if they want to dialogue. If they agree on that, and we are satisfied, then we shall go into dialogue and listen to them by way of ideas [but] those votes can never be thrown away."
The MDC denounced the pre-condition as a joke.
"This is an unrealistic precondition and we are not going to accept it," Nelson Chamisa, the party spokesman, said on Friday.
Mbeki has been fiercely criticised by the MDC over his consistent refusal to publicly criticise his Zimbabwean counterpart. However, Mugabe Mugabe has said "we are happy that Mbeki continues to be the facilitator," adding "he has done nothing wrong".