Morgan Tsvangirai told his first news conference since Saturday's elections that he was waiting for an official announcement of election results before he would enter any discussions.
"Our country is on a precipice, on a cliff edge," he said.
A businessman close to the Zimbabwe Electoral Commission, or ZEC, and a lawyer close to the opposition said earlier that aides of Mugabe and Tsvangirai were discussing how Mugabe could relinquish power.
The rivals' advisers were discussing a "transitional arrangement," the lawyer said. Both sources spoke on condition of anonymity because of the sensitivity of the issue.
"There are no discussions," Tsvangirai said. "Let's wait for ZEC to complete it's work, then we can discuss the circumstances that will affect the people."
Independent observers say trends indicate Tsvangirai won the most votes in the presidential race, but not enough to avoid a runoff - a prospect that could be humiliating to the 84-year-old president after 28 years in power.
The military is divided within its own ranks, with some leaders more eager to see Mugabe go than others. But, CBS News reporter Sarah Carter says, there does now seem to have been a clear warning from senior military leaders that if Mugabe attempts to manipulate the results of a defeat in order to stay in office, he will do so without the backing of the defense forces.
On the streets of Harare and across Zimbabwe, "the army has not been steadfastly supporting Mugabe as one would expect," Carter reports. She says many in the region expected Mugabe to steal this election and the fact that the limited official results made available are so close has come as a surprise.
The real question, says Carter, is what Zimbabwe's senior military leaders will do should Mugabe unexpectedly declare an election victory, in spite of all the evidence that his opponents have won. They only told the president he would lose their support if he loses the election and, officially, that is still far from clear.
No returns from the presidential vote have been made public, fueling fears of rigging. Mugabe has been accused of stealing past elections, though that was before Zimbabwe's economy collapsed and leading members of his own party openly defied him.
Tsvangirai claimed to have won more than the 50 percent simple majority needed to avoid a runoff. He urged the electoral commission "to proceed with haste, and I think 2 1/2 days is not haste at all."
The businessman said Mugabe has been told he is far behind Morgan Tsvangirai in preliminary results of Saturday's presidential elections and that there could be an uprising if Mugabe were declared the winner.
He said Zimbabwe's security chiefs have told the Electoral Commission to issue results portraying a close race, to prevent celebrations that could ignite violence.
The commission has released results for 142 of the 210 parliamentary seats - giving Tsvangirai's Movement for Democratic Change 72 seats, including five for a breakaway faction, and 70 for Mugabe's party.
Martin Rupiya, a military analyst at South Africa's Institute for Strategic Studies and a former lieutenant-colonel in the Zimbabwe army, said he had heard of the military's involvement in negotiations for Mugabe to step down.
The election outcome "has compelled the military, the hawkish wing and the other moderate, to begin to reconsider accommodating the opposition," he said. "Because of the nature of the wins they have been forced to reassess."
John Makumbe, a political scientist at the University of Zimbabwe, said he had learned from military sources that they would honor the results of the elections. The security chiefs last week warned they would not serve anybody but Mugabe and would not tolerate an opposition victory.
At the news conference, Tsvangirai spoke as if he already had been declared president:
"For years we have trod a journey of hunger, pain, torture and brutality," he said. "Today we face a new challenge of governing and rehabilitating our beloved country, the challenge of giving birth to a new Zimbabwe founded on restoration not retribution, on love not war."
He said his party would release its own complete tallies Wednesday.
The opposition has claimed victory based on results posted outside polling stations, including in several rural strongholds of Mugabe. The initiative to display the results on voting station doors was part of an agreement between the parties negotiated by South African President Thabo Mbeki, and could make it more difficult to cheat.
The European Union said it wants Mugabe to step down to spare his nation political turmoil.
"If Mr. Mugabe continues, there will be a coup d'etat," said Slovenian Foreign Minister Dimitri Rupel, whose country holds the EU presidency. He said he hoped Mugabe "is on his way out."
British Prime Minister Gordon Brown called for the immediate release of election results.
"Results should be published immediately and the elections must be seen to be fair," Brown told reporters in London. "It's very important that the democratic rights of the Zimbabwe people be respected and upheld and recognized."
The Netherlands hailed the possibility of an opposition victory.
"I get the impression that the Zimbabweans have voted for change and democratic forces have the upper hand," said Dutch Foreign Minister Maxime Verhagen. "Now, finally, the people of Zimbabwe have the prospect of a better life."
The Zimbabwe Election Support Network, a coalition of 38 Zimbabwe civil society organizations, said its random representative sample of polling stations showed Tsvangirai won just over 49 percent of the vote and Mugabe 42 percent. Simba Makoni, a former Mugabe loyalist, trailed at about 8 percent.
Mugabe would have to weigh the concerns of those who have profited from his patronage, a group that includes top military leaders, party officials and business people. They receive mining concessions, construction contracts and preferential licenses to run transport companies and other businesses.
Marwick Khumalo, head of the Pan-African Parliament observer mission, told South African radio Tuesday that leading members of Mugabe's party were contemplating defeat with trepidation.
"I was talking to some of the big wigs in the ruling party and they also are concerned about the possibility of a change of guard," Khumalo said. "ZANU-PF has actually been institutionalized in the lives of Zimbabweans, so it is not easy for anyone within the sphere of the ruling party to accept that 'Maybe we might be defeated or might have been defeated."'
Mugabe led a guerrilla movement that fought a seven-year war to end white minority rule. At independence, he was hailed for his policies of racial reconciliation and development that brought education and health to millions who had been denied those services under colonial rule. Zimbabwe's economy thrived on exports of food, minerals and tobacco.
The unraveling began when Mugabe ordered the often-violent seizures of white-owned commercial farms, ostensibly to return them to the landless black majority. Instead, Mugabe replaced a white elite with a black one, giving the farms to relatives, friends and cronies who allowed cultivated fields to be taken over by weeds.Today, a third of the population depends on imported food handouts. Another third has fled the country as economic and political refugees and 80 percent is jobless. Life expectancy has fallen from 60 to 35 years and shortages of food, medicine, water, electricity and fuel are chronic.
The economy is in dramatically worse shape than during past elections, driving other changes in Zimbabwe's political landscape. The candidacy of Makoni, a former finance secretary, drew open support from other leaders in the ruling party.