Mugabe stunned the world and sparked confusion in Zimbabwe when he used a televised address - widely expected to be a resignation speech - to claim that the soft military coup against him did not represent a challenge to his authority and that he would preside over the party's December congress as previously planned.
Chris Mutsvangwa, the head of the country's influential veterans association, called Mugabe's refusal to stand down a "dereliction of duty" and said his organisation would bring thousands of people back onto the streets in response.
"We were disappointed yesterday in the midst of all those generals he appeared to swap [speeches]" he said at a press conference on Monday morning, referring to footage that showed Mugabe shuffling a sheaf of A4 sheets before he began speaking on Sunday.
Addressing Mugabe directly, he added: "Your time is up."
Mugabe has been under effective house arrest since the Zimbabwean military seized control of the country in a coup designed to prevent him from installing his wife, Grace, as his successor.
In an effort to retain a semblance of legitimacy for their actions, the generals have attempted to persuade Mugabe to resign in accordance with the country's constitution rather than to simply oust him in a classic coup d'etat.
Tens of thousands marched through Harare demanding his resignation and Zanu PF has recalled him as leader of the party, though it has not expelled him.
MPs from Zanu PF gathered in Harare to discuss removing Mugabe from office via a parliamentary vote of no confidence after he ignored a deadline to step down.
The party had demanded that Mugabe resign by midday local time (10am GMT).
MPs from the Movement for Democratic Change, Zimbabwe's main opposition party, said they would meet on Tuesday (local time) to agree a position on a possible impeachment vote.
Morgan Tsvangirai, the leader of the MDC, warned that infighting inside Zanu PF and differences with the military over how to handle the crisis should not be allowed to prevent a "fresh start" for the country.
"It would be inimical to progress and the future of the country if all this action was about power retention at all costs," Tsvangirai wrote on his party's website.
Zimbabwe's constitution allows Parliament to remove the president if two thirds of both houses find him unfit to carry out his duties.
Parliament first would have to vote by a simple majority to appoint a select committee to investigate Mugabe's fitness to rule.
British PM Theresa May said that it was clear Mugabe had lost the support of the Zimbabwean people but that the outcome of the crisis remained uncertain.
"We don't yet know how developments in Zimbabwe are going to play out. What does appear clear is that Mugabe has lost the support of the people and of his party," said James Slack, May's spokesman.
Slack said Britain "would appeal for everyone to refrain from violence and hope to see a peaceful and swift resolution to the situation".
Kenneth Kaunda, a former president of Zambia, was expected to arrived in Harare on Monday in a bid to persuade Mugabe to make a "dignified" exit.
