The governing ZANU-PF party, which held emergency talks at its headquarters in the capital, Harare, to consider the fate of the president who had ruled for 37 years, appointed the previously fired vice president, Emmerson Mnangagwa, as Mr. Mugabe’s successor.

Under the Constitution, Mr. Mugabe remains president, even if in name only. But if he does not resign by noon Monday, the committee members decided, he would face impeachment by Parliament.

Cheers and dancing broke out in the building after the vote, according to video shared on social media.