Mr Mbeki has said it is too early for outside intervention.
Gordon Brown is to hold private talks with South African President Thabo Mbeki over the crisis in Zimbabwe.
As Zimbabwe's most important neighbour and ally Mr Mbeki is seen as one of the few world leaders capable of exerting influence on Robert Mugabe.
But he has been reluctant to criticise Zimbabwe's president and has rejected calls for international intervention.
Mr Mbeki came to Britain for the Progressive Governance summit of centre left leaders which ended on Saturday.
Speaking about Zimbabwe at the close of the conference in Watford, he said: "The situation for now is manageable.
"It is time to wait. Let's see the outcome of the election results. If there is a re-run of the presidential election let us see what comes out of that."
He defended how the disputed elections have been conducted so far and said the delay in announcing the result of the presidential ballot was due to the lengthy verification process put in place by the Zimbabwe Electoral Commission.
But BBC political correspondent Rajini Vaidyanathan said he also betrayed frustration amid a barrage of questions about Zimbabwe, declaring: "Zimbabwe is not a South African province. Can we agree about that?"
Our correspondent said Mr Mbeki will be determined to avoid any suggestion he was being dictated to by Western powers such as Britain or America.
But Mr Brown, who has repeated his calls for the election results to be announced immediately, will be hoping to win him round during private talks.
The PM said if there was a run-off between Mr Mugabe and Mr Tsvangirai, international observers should be in place to ensure it was fair.
"We are monitoring the situation closely. I think the important thing is that the results have got to be published. They cannot be any longer delayed. They have got to be seen to fair," he said.
Foreign Secretary David Miliband said the UN Security Council was united in wanting the results announced.
Opposition leader Morgan Tsvangirai, leader of the Movement for Democratic Change, has accused Mr Mugabe of preparing to wage a "war against the people" of Zimbabwe.
The MDC has urged the UN to intervene to prevent bloodshed, if there was a final run-off between Mr Mugabe and Mr Tsvangirai for the presidency.