After two hours with presidents Thabo Mbeki of South Africa and Bakili Muluzi of Malawi and Nigerian president-elect Olusegun Obasanjo, Mugabe told a press conference that he would only consent to talks with Tsvangirai's Movement for Democratic Change (MDC) if the party formally "recognised" him.
This meant the MDC would have to drop its court challenge to the results of last year's controversial presidential election in which Mugabe was declared the winner.
Most Western governments, the Commonwealth and the parliamentary observer group of the Southern African Development Community say the vote was not fair and that Mugabe had won through violence and fraud.
The MDC insists that the fraudulent elections do not give Mugabe legitimacy to rule the country and the party refuses to recognize him as president.
Obasanjo told journalists that the three visiting leaders were "delighted" President Mugabe and his government are "very anxious" for negotiations.
"There is a little point (the MDC's court challenge) which we can work out. We will work on it as quickly as possible".
The MDC issued a statement, which made no direct mention of the court challenge.
It said the three leaders had said there was "a pressing need for Zimbabweans to open dialogue with a view to addressing all economic, political and social problems besetting Zimbabwe".
"The MDC reiterated that it was ready to (for) unconditional dialogue and was ready any time, anywhere to engage in such dialogue".
Earlier, riot police arrested about seven MDC supporters as they tried to demonstrate support for the MDC outside the Sheraton Hotel where the three visiting leaders met Tsvangirai.
Most foreign correspondents and reporters from the local independent press were refused access to State House, Mugabe's official residence, where the three met Mugabe.
They were also refused admission to the press conference addressed by Obasanjo and Mugabe.
Mbeki has said that the initiative aimed to bring Mugabe and Tsvangirai together in dialogue to try and resolve the country's increasingly volatile crises, as the once robust economy collapsed and law and order disintegrated.
Tsvangirai said he was ready to talk to Mugabe on condition that the rule of law was restored.
Mugabe's administration has been taking an increasingly hard line in the last week, and appears to be insisting it will not talk to Tsvangirai.
While the leaders talk, ordinary Zimbabweans face an accelerating crash in living standards as famine sets, inflation is forecast to reach 400 percent at the end of the year, fuel supplies dry up and critical shortages of basic food commodities continue.
On Sunday, the state-owned press declared that Mbeki and Obasanjo were not to be trusted as they might be coming to Harare as "British agents ... to play British games".
This week United States Assistant Secretary of State for Africa Walter Kansteiner will be in neighbouring Botswana for a trade initiative, and later in South Africa.
He denied last week that "regime change" was on the United States' agenda for Zimbabwe.
He said the restoration of "legitimacy" was the most crucial issue and would require a transitional government followed by free and fair internationally monitored elections.
If Mugabe contested the elections and won, he said, "then so be it". - Sapa
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