Mbeki wants the crisis resolved regionally through the Southern Africa Development Community, which has so far avoided a tough stand and for which he has unsuccessfully mediated in Zimbabwe in the past.
However the UN secretary-general said this was not enough.
"The Zimbabwean authorities and the countries of the region have insisted that these matters are for the region to resolve but the international community continues to watch and wait for decisive action," he said.
Gordon Brown, the prime minister of Britain, Zimbabwe's former colonial power, also told the summit: "No one thinks, having seen the results of polling stations, that President Mugabe has won."
"Let a single clear message go out from here in New York that we ... stand solidly behind democracy and human rights for Zimbabwe," he added.
UN representatives from the US, Italy and France also called for results to be released.
"The international community continues to watch and wait for decisive action"
Ban Ki-moon, UN secretary-general
Jacob Zuma, president of South Africa's ruling African National Congress, said on Wednesday that the delay in the release of results "increases anxiety each day".
Zimbabwe held a presidential election on March 29, which Morgan Tsvangirai of the Movement for Democratic Change (MDC) party says he won.
However the ruling Zanu-PF party under President Robert Mugabe says he did not gain enough votes and a run-off should be held.
The electoral commission says it is still verifying the votes.
Country in crisis
Zimbabwe, once the "breadbasket" of southern Africa, is currently experiencing 80 per cent unemployment, chronic food shortages, and the world's worst rate of inflation of almost 165,000 per cent.
Critics blame Mugabe for the economic crisis and say the country's misery will only end when he is replaced.
However Mugabe says much of the blame should be placed with Zimbabwe's former colonial power, which he accuses of interfering in the nation's affairs because of his plans to seize white-owned farms.
Wednesday's session at the UN was supposed to have discussed efforts by the UN and the African Union to provide solutions to Africa's conflicts in regions such as Darfur in Sudan and Somalia.