JOHANNESBURG  President Robert Mugabe of Zimbabwe and the opposition leader Morgan Tsvangirai struck a power-sharing deal on Thursday after more than a month of wrangling, but it was still far from clear how the bitter foes would divide the authority to govern.

The agreement, brokered by President Thabo Mbeki of South Africa, signals that Mr. Mugabe may be willing to cede some authority to Mr. Tsvangirai, loosening the tight grip on power he has maintained for nearly three decades and easing the political crisis that has engulfed Zimbabwe for months.

They did not spell out how the deal would work, but Mr. Mbeki said the details of the agreement would be released Monday at a signing ceremony. Officials in both the governing and opposition parties described an arrangement that seemed to leave neither man clearly in charge. That may reduce the chances that the accord will bring stability and attract the foreign aid needed to rebuild the country’s ruined economy.

Under the agreement, officials said, Mr. Tsvangirai would become prime minister and oversee a council of ministers that would formulate and carry out policies. Mr. Mugabe would retain his title of president and would lead a cabinet of the ministers that would supervise the council. That arrangement appears to give both men the power to oversee the same group of ministers.