Correspondents say it could be the last chance for Mr Mbeki's mediation
Zimbabwe's President Robert Mugabe has said power-sharing talks to resolve the political crisis are "moving forward".
A spokesman for the opposition Movement for Democratic Change said parties were trying to narrow their differences.
The latest round of talks mediated by South African President Thabo Mbeki in Zimbabwe's capital Harare began on Monday and is due to end on Wednesday.
Both parties have hardened their positions since the previous round of talks broke down last month.
Mr Mbeki has led regional efforts to broker a deal over Zimbabwe's disputed election, which both Mr Mugabe and MDC leader Morgan Tsvangirai claim to have won.
South Africa's national broadcaster, the SABC, reports that a fresh document has been tabled providing the opposition leader with more power, as an executive prime minister.
Earlier, Mr Mugabe had said he was ready to form a government alone, while Mr Tsvangirai had said there should be new elections if a deal was not reached.
Zimbabwean journalist Brian Hungwe reports that this time, Mr Mbeki is said to have brought a new power-sharing proposal with him when he arrived in Zimbabwe on Monday.
Zimbabwe's state-run Herald newspaper cited an unnamed source as saying that an "extensive" document had been submitted to parties.
Morgan Tsvangirai has said no deal would be better than a bad one
"President Mbeki has submitted a document that looks at the executive powers and their distribution while it also looks at the structure of an all-inclusive government if the parties agree to it," the newspaper said.
But MDC insiders are pessimistic about the chances of a quick solution, Brian Hungwe says.
After a six-hour session in a Harare hotel on Monday Mr Mugabe said there had been no deal, but that "we are moving forward, we are not going back".
"It was a good meeting," he said.
Mr Tsvangirai did not comment but MDC spokesman Nelson Chamisa said parties were trying to find "areas of consensus".
Before last month's talks broke down, the two rivals had agreed that Mr Tsvangirai would be named prime minister while Mr Mugabe remained president, but they could not agree on how to share powers.
The MDC leader gained more votes than Mr Mugabe in March elections but official results say he did not pass the 50% threshold for outright victory.
Mr Tsvangirai pulled out of the June run-off, saying some 200 of his supporters had been killed and 200,000 forced from their homes in a campaign of violence led by the army and supporters of the ruling Zanu-PF.
Zanu-PF has denied the claims and accused the MDC of both exaggerating the scale of the violence and being responsible for it.