The two leaders appeared cordial as they met in Harare
South African President Thabo Mbeki has called for patience over unreleased poll results in Zimbabwe, after talks with its president, Robert Mugabe.
They met after Mr Mugabe said he would not attend a summit that has opened in Zambia aimed at ending deadlock over presidential elections two weeks ago.
Opposition leader Morgan Tsvangirai says he won the vote, and hopes leaders will pressure Mr Mugabe to step down.
Despite growing tensions, Mr Mbeki said there was "no crisis" in Zimbabwe.
Mr Mugabe's Zanu-PF party lost its House of Assembly majority for the first time since 1980 in the 29 March poll, but no results have yet been released from the presidential race.
Mr Mbeki said everyone should wait for the results to be published.
"If nobody wins a clear majority the law provides for a second run. If that happens I would not describe it as a crisis. It's a normal electoral process," he said.
Correspondents say the summit, held by the Southern African Development Community (SADC), can achieve little without Mr Mugabe there, which is why Mr Mbeki stopped in Harare first.
SOUTHERN AFRICAN DEVELOPMENT COMMUNITY
Member countries: Angola, Botswana, DR Congo, Lesotho, Madagascar, Malawi, Mauritius, Mozambique, Namibia, South Africa, Swaziland, Tanzania, Zambia and Zimbabwe
Aims: Development, economic growth, regional integration, common political values and systems, promote peace and security
Role in Zimbabwe: Appointed South African President Thabo Mbeki to mediate in 2007 - new election law agreed but MDC later said talks had failed; sent election monitors for recent polls
Mr Mbeki has led mediation efforts between the two Zimbabwean sides since last year, but his "quiet diplomacy" approach has been criticised by some as ineffective.
The BBC's Peter Greste, in Johannesburg, says that rather than risking a public rebuke from his colleagues in Zambia, President Mugabe is sending a delegation of government ministers.
The state-run Herald newspaper quoted Foreign Affairs Secretary Joey Bimha as calling the summit "unnecessary" because the votes were still being counted.
Justice Minister Patrick Chinamasa, part of Zimbabwe's delegation to the summit, told AFP news agency that his country would not accept Mr Tsvangirai's participation in the meeting.
"Inviting an opposition leader to a heads of state meeting is unheard of," he said.
Ahead of the summit, the opposition Movement for Democratic Change (MDC) urged the African leaders to "speak strongly and decisively against the dictatorship".
MDC Secretary-General Tendai Biti said Zimbabwe was "at a crossroads" and the summit was a "critical meeting" for his country and the region.
The summit comes amid growing pressure on Mr Mugabe to release the results of the presidential poll.
UK Prime Minister Gordon Brown made his most scathing comments yet on Mr Mugabe.
The SADC summit comes amid growing tension in Zimbabwe
"I cannot understand why it is taking so long to announce the result of the presidential elections," Mr Brown said in a statement released late on Friday.
"I am appalled by the signs that the regime is once again resorting to intimidation and violence."
He said "the international community's patience with the [Mugabe] regime is wearing thin".
Mr Mugabe responded on Saturday by saying: "I know Brown, he's a little tiny dot, eh? On this world."
UN Secretary General Ban Ki-moon congratulated the SADC for "their timely initiative".
"The secretary general is concerned that the situation in Zimbabwe could deteriorate if there is no prompt action to resolve this impasse," UN spokeswoman Marie Okabe said.
Mr Ban's predecessor, Kofi Annan, also called for the SADC leaders to push for "a peaceful and just solution".
"They have a grave responsibility to act; act not only because of the negative spillover effects on the region, but also to ensure that democracy, human rights and the rule of law are respected."
He warned that Zimbabwe was standing "on the brink".
Zimbabwean police have banned political rallies "with immediate effect", amid growing tension over the disputed election.
Zimbabwe's police warned political parties against "creating mayhem"
The MDC has called for a strike starting on Tuesday to pressure the authorities.
Mr Tsvangirai has been touring southern Africa, urging leaders to put pressure on Mr Mugabe to step down.
He says he won the vote outright and has refused to take part in any run-off with Mr Mugabe.
Mr Tsvangirai has accused Mr Mugabe of mobilising Zimbabwean security forces and pro-Zanu-PF forces to intimidate MDC voters.
He also accuses Mr Mugabe of interfering with the work of the Zimbabwe Electoral Commission.
Mr Mugabe has ruled Zimbabwe since independence from Britain in 1980.