HARARE, Zimbabwe — South Africa’s president said yesterday he has mediated a power-sharing deal between Zimbabwean President Mugabe and the opposition.

President Mbeki did not offer details, but said the agreement would be signed Monday. Opposition leader Morgan Tsvangirai also told reporters the parties “have got a deal.”

Mr. Mbeki has been in Zimbabwe since Monday trying to work out how Messrs. Tsvangirai and Mugabe would run a unity government.

The key stumbling block has been how the two rivals would divide responsibilities and who would have the most authority.

Mr. Tsvangirai has said he should be head of government and preside over Cabinet meetings, while Mr. Mugabe should be relegated to a ceremonial position. But Mr. Mugabe had shown little willingness to give up much of the power he has held since independence from Britain in 1980.

Mr. Tsvangirai’s party won the most votes in legislative and presidential elections in March, but he did not win enough to avoid a runoff against Mr. Mugabe. An onslaught of state-sponsored violence against Mr. Tsvangirai’s supporters forced him to drop out of the presidential runoff.

Mr. Mugabe subsequently was the only candidate in a presidential runoff, which Western nations widely denounced as a sham.

Much of Mr. Mugabe’s popularity at home and across the continent is linked to his image as a proud African leader unafraid to defy the West. Mr. Tsvangirai, who lacks Mr. Mugabe’s anti-colonial credentials, has said Zimbabwe needs to work with the West to overcome its economic and political crises.

A political settlement would free the leaders to address Zimbabwe’s severe economic problems — which include having the world’s highest inflation rate and chronic food and fuel shortages.

Foreign investors have been wary because of the political uncertainty. Western governments are poised to help with grants and loans, but will not deal with Mr. Mugabe, who they denounce as a dictator.