The Southern African Development Community (SADC) had asked Mbeki last week to spearhead efforts to resolve the crisis, which has deepened since Mugabe's violent crackdown on political opponents last month.
Mbeki dismissed suggestions that Zimbabwe's neighbours could force change in the country. "We don't have a big stick," he said.
He said a joint approach by African leaders could pave the way to a settlement.
Mbeki said his office had already been in contact with both factions of the opposition Movement for Democratic Change (MDC) and Zanu-PF to draw up a negotiating framework for next year's elections, in which Mugabe has already been endorsed as the Zanu-PF candidate.
Mbeki said the talks would probably focus on MDC demands for legal and electoral reforms, including the strict media and security laws which critics say Mugabe has used to entrench his power in the country.
"I am quite clear from previous interactions with the MDC we have had they will raise questions ... like legislation affecting the media, legislation about holding of public meetings.
"We will then engage Zanu-PF, saying it is necessary to respond to all of these. We may very well come to a stage later when they will have to sit together to agree ... [on] what they will do to create a climate conducive to free and fair elections."
The Zimbabwe Congress of Trade Unions (ZCTU) had called the strike to press for a minimum workers' wage of a million Zimbabwe dollars ($4,000 on the official market but worth $50 on the black market), an end to the country's economic meltdown and for better access to Aids drugs.