BBC News, Johannesburg
They are meeting to discuss ways of improving co-operation between the African Union and the United Nations. The issue has never been more timely. South Africa's president has been the point-man for the region's, and the world's, diplomatic efforts to resolve Zimbabwe's increasingly desperate crisis. He has also staked his legacy on success in Zimbabwe.
He argues that the rest of the world should butt out and let Africans resolve the problems in an African way. Western finger-wagging, he says, simply does not help. Although Zimbabwe is not officially on the agenda, diplomats from the United States and Britain are determined to make it so.
And in a not-so-subtle attempt to catch the Security Council's eye, one organisation is planning to fly a 3,000-sq-ft (280-sq-m) banner above the UN on Wednesday morning, calling on Mbeki to convince Zimbabwe's leader Robert Mugabe to respect the will of his people.
The banner, with some 120,000 signatures, is likely to be the latest in a loud chorus of international demands to "do something" about democracy in Zimbabwe. Over the weekend, it was UK Prime Minister Gordon Brown's turn, declaring: "We can't wait any longer for the announcement of these results."
The US said it had "credible reports of violence and intimidation" against opposition supporters and called on the government to end the attacks.
Zimbabwe is an easy target for Western governments. The image of Robert Mugabe as an arrogant dictator is straightforward and easy to condemn. Doing so polishes politicians' credentials as democrats defending human rights, without having to worry about losing things like oil. But the bitter lesson of the past decade has been that in being openly critical, the West has done more harm than good in Zimbabwe.
Starting with former UK Prime Minister Tony Blair and his then International Development Secretary Clare Short more than a decade ago, British criticism has played into President Mugabe's view of black Africa under siege by white colonialists. Rather than increasing pressure for him to go, the criticism has given Mr Mugabe fuel for his rhetorical fire.
In 1997, Ms Short wrote a now infamous letter to Zimbabwe's Agriculture Minister, Kumbirai Kangai. She was responding to President Mugabe's demand that Britain fulfill its Lancaster House agreement to pay for land redistribution from white farmers to poor black Zimbabweans.
"I should make it clear," she said, "that we do not accept that Britain has a special responsibility to meet the costs of land purchase in Zimbabwe."
"We are a new government from diverse backgrounds without links to former colonial interests. My own origins are Irish and, as you know, we were colonised, not colonisers."
It hardly matters now whether that letter really did send Mr Mugabe into a rage that became focused on the white farmers who were to lose their properties in the land invasions that began in 2000.
But it showed a basic misunderstanding of Zimbabwe's recent colonial history that still taints the West's approach to the country. After Zimbabwe's liberation war of the 1970s to overthrow Ian Smith's minority government, the white community reached an unspoken compact with President Mugabe's Zanu-PF party.
If they stayed out of politics, they would be left alone. But when the issue over land flared up, they began to support the opposition Movement for Democratic Change (MDC) in a move that Mr Mugabe came to regard as a continuation of the war by other means. It became easy to cast the MDC as poodles of London and Washington, particularly as it accepted support from both.
Now, every utterance from either capital confirms a view of the West as one that still cannot accept the idea that Africans should be allowed to shape their own destinies. That is what Mr Mbeki meant when he said on Sunday that "there is no crisis". One of his negotiating team, Sydney Mufamadi, said he understood the anxiety about the delay in releasing election results.
But he added: "Those of us that have a responsibility to make sure a resolution is found, also have a responsibility to say that we have not reached a dead end because we know what processes can still be activated to remove the blockage."
The need to keep control of this crisis within African hands may also explain why the region's leaders have been so reluctant to openly criticise Mugabe.
In this, they are oddly out of step with public opinion, and in Thabo Mbeki's case even within his own party. On Tuesday, President Mbeki's African National Congress released a statement that described the situation in Zimbabwe as 'dire', and as having a negative impact on all of southern Africa.
The statement did not attack the president directly of course, but it was an implicit criticism of his policy of 'quiet diplomacy' and that widely derided 'no crisis' remark. The frustration with the situation is not just limited to South Africa. If the newspaper columns are any indication, neighbouring states firmly believe that Zimbabwe's 84-year-old leader should go as soon as possible.
But the cost to the dignity of leaders like Mr Mbeki to be seen to be heeding their former colonial masters is too much to bear. Southern African countries are painfully aware of the impact of Zimbabwe's collapse. They are hosting some three million Zimbabweans and these are states that can barely afford to feed themselves. Yet African solidarity still seems to be the defining theme of regional diplomacy.
The leaders of the Southern African Development Community (Sadc) spent more than 12 hours in a summit that finally ended at 0500 on Sunday - more than 11 hours later than scheduled.
Sources suggest there was a fierce debate over whether the situation constituted a "crisis" or not, and about whether there should be some kind of government of national unity. The final communique said there was no crisis, and blandly called on the Zimbabwe Electoral Commission to release the results "as expeditiously as possible".
And that may be where Sadc focuses its efforts. In his briefing, mediator Sydney Mufumadi said Sadc understood it had to follow up its words with actions, and that in urging a "safe environment" for a runoff, it would have to work to make that happen.
That chimes with opposition leader Morgan Tsvangarai's most recent statement in which he said he would take part in a run-off after all, but only if the electoral environment were indeed safe and secure, and as long as international mediators tracked the whole process from start to finish.
It is a small concession, but it may yet prove crucial if those conditions are met. None of this is to suggest that the West should sit on its hands. But if history is anything to go by, UN pressure may only make it harder to resolve the crisis.