Mr Tsvangirai left the talks without comment
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Zimbabwean President Robert Mugabe has said that 14 hours of talks with the opposition have ended inconclusively.
However, Mr Mugabe said the talks would continue later on Monday, adding he was "confident" a deal could be reached.
South African President Thabo Mbeki has been acting as mediator at the talks, which began on Sunday morning at a hotel in Zimbabwe's capital, Harare.
Opposition leader Morgan Tsvangirai declined to comment as he left the hotel following the meeting.
The key issue at the talks is how much power Mr Mugabe will hold, and what role Mr Tsvangirai will take on.
One widely touted solution is that Mr Mugabe, the Zanu-PF leader, may become ceremonial president while Mr Tsvangirai, leader of the opposition Movement for Democratic Change (MDC), becomes executive prime minister.
Chairs and bouquets of flowers had been set up on Sunday in a room at the hotel where the talks are taking place in anticipation of a breakthrough.
Monday is Heroes' Day in Zimbabwe, honouring those who died in the 1970s guerrilla war against white minority rule.
Mugabe's role
"We're not through yet, but we've taken a break," said President Mugabe, as he left the talks late at night.
A key issue at the talks is the future role for Mr Mugabe
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Asked if sticking points remained, he said: "There are always sticking points in any dialogue, but we are confident we will overcome."
The talks bring together Mr Mugabe and Mr Tsvangirai, as well as Arthur Mutambara, the leader of a smaller MDC faction.
Mr Mbeki had been mediating negotiations between Mr Mugabe and the opposition in neighbouring South Africa, and arrived in Harare on Saturday in what a Zimbabwean government spokesman called an "important milestone".
The talks started on Sunday morning with Mr Mbeki meeting all three politicians separately, before bringing them together, Mr Mutambara's spokesman said.
Mr Mugabe won a run-off in June after Mr Tsvangirai pulled out of the race alleging violence against his backers.
South African mediators say that talks are aimed at creating some form of coalition but there is disagreement over who would lead a unity government and over Mr Mugabe's exact role.
Make or break
For the two men to achieve a power-sharing deal will be no easy matter, as they share nothing but a mutual loathing, says BBC Africa analyst, Martin Plaut.
Mr Mbeki (left) is hoping to secure a power-sharing deal
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Assuming a deal can be achieved, the next question is how the senior figures in the country's security apparatus - the military and police - can be accommodated, our analyst adds.
There were strong suggestions a deal was blocked earlier this year because their concerns had not been addressed.
This time round it is proposed that there would be two deputy prime ministers: - one - to be occupied by the ruling Zanu-PF, would take the defence portfolio
- the other, for the MDC, would take the police
If this is acceptable to all sides, our analyst suggests, then other issues are seen as less important.
Mr Mbeki is under pressure to achieve a solid outcome ahead of a mid-August summit of the Southern African Development Community (Sadc).
Hundreds of thousands of Zimbabweans have fled the country's worsening political and economic situation, many crossing over the borders into neighbouring states of South Africa, Zambia and Botswana.
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