HARARE, Zimbabwe — Former loyalists of President Robert Mugabe of Zimbabwe vowed on Monday to begin impeachment proceedings against him, after he ignored their ultimatum demanding that he step down.

About 230 of 260 lawmakers from ZANU-PF, the political party Mr. Mugabe led from 1977 until his expulsion on Sunday, met at the party’s headquarters in Harare, the capital, and agreed to begin impeachment proceedings on Tuesday — a process that could take weeks.

The protracted negotiations between military leaders who seized power on Wednesday and Mr. Mugabe have frustrated Zimbabweans who had hoped for a quick resolution to the standoff, most likely involving Mr. Mugabe’s resignation and, perhaps, exile. If the military was hoping that the party’s intervention might end the standoff, such hopes appeared to be dashed on Monday.

Though visibly enfeebled, Mr. Mugabe, 93, has shown the negotiating skills that have kept him in power for 37 years. He gave a televised address on Sunday in which he stunned his nation by not announcing his resignation. On Monday, the head of the military said that Mr. Mugabe had been in touch with his estranged deputy, Emmerson Mnangagwa, the vice president whose firing set off the chain of events leading to the military intervention last Wednesday that took Mr. Mugabe into custody.