Mr Mbeki has said it is too early for outside intervention.
Gordon Brown has held private talks with South African President Thabo Mbeki over the crisis in Zimbabwe.
Mr Brown spent more than two hours trying to persuade Mr Mbeki to use his influence to end the situation.
A Number 10 spokesperson said the private meeting had involved "in depth" discussions on the issue.
Meanwhile Robert Mugabe's party has asked Zimbabwe's electoral officials to delay presidential poll results to check "errors and miscalculations".
As he left Downing Street, reporters asked Mr Mbeki whether there had been any progress, to which he replied: "I don't know, we will see."
As Zimbabwe's most important neighbour and ally Mr Mbeki is seen as one of the few world leaders capable of exerting influence on President Robert Mugabe.
But he has been reluctant to criticise the Zimbabwean leader 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."