The ultimatum given to the veteran leader, who has been in power for 37 years, came five days after the military seized power and placed Mugabe under house arrest.
The embattled 93-year-old leader has so far appeared resistant to demands to step down, but is increasingly running out of options.
On Sunday, the ruling ZANU-PF party dismissed Mugabe as its leader and also expelled his wife, Grace, from its ranks.
It said if Mugabe does not resign by midday on Monday, then it will start impeachment proceedings when parliament resumes on Tuesday.
Members also voted to name the sacked Vice President Emmerson Mnangagwa, whom Mugabe fired on November 6, as new party leader.
‘Let the old man resign and go home’
In opening remarks at ZANU-PF’s Central Committee meeting, Obert Mpofu, the minister of home affairs who chaired the gathering, blamed First Lady Grace Mugabe and her allies for taking advantage of the veteran leader.
The rise and fall of Zimbabwe’s Robert Mugabe
“We meet here today with a heavy heart because Mugabe’s wife and her close associates have taken advantage of his frail condition and abused the resources of the country,” he told members. “I warmly welcome you all to this historic meeting which will mark a new era, not only for our country but for the party.”
Members cheered as the resolution to recall Mugabe was read out.
“It will be very honourable for him to resign than to face impeachment,” a war veteran in the capital, Harare, told Al Hazeera.
“It will continue to soil his record – and that’s our advice, please let the old man resign and go home.”
Earlier on Sunday, the ZANU-PF Youth League, which Grace Mugabe leads, called for her expulsion from ZANU-PF “forever” and demanded the president to resign as leader of the country and party, “so that he can rest as the elderly statesman he is”.
The group also condemned the “unprocedural expulsion” of Mnangagwa.
Mugabe has been under military quarantine at his residence since Wednesday.
ay, when the army placed him under house arrest and took over state TV and key government sites.
Mugabe’s decision to sack Mnangagwa, who was touted as his most likely successor, spurred an internal power struggle.
First Lady Grace Mugabe was tipped to takeover as second secretary and vice president, prompting a military takeover with the army saying it wanted to “target criminals” around Mugabe who were leading the party and state astray.
In a rare sign of solidarity between the people and the army, which has often been a pillar of support for Mugabe’s near 40-year rule, Zimbabweans on Saturday expressed support and praise for the military’s operation.
Huge crowds swelled on the streets.
Civilians could be seen giving hugs and fist bumps to soldiers, and taking selfies with army personnel camped outside parliament, the presidential offices and other strategic sites.
There was a convivial mood in the capital as people played loud music and danced after marching to State House to demand Mugabe’s resignation, in scenes described as “historic” and representing a “day of freedom”.
Zimbabweans have never before gathered in such numbers to march against Mugabe.
‘It’s very hard’
Patrick Chinamasa, a senior ZANU-PF official and former minister, said he was expecting “cooperation” from Mugabe following the “overwhelming decision” taken by the ruling party’s central committee and Saturday’s “massive demonstration”.
Zimbabwe crisis: Tens of thousands demand ‘Mugabe must go’
“It will make the transfer of power smooth and it will be very good for our country if in fact we were able to achieve it without any prolonged and protracted procedure,” he told Al Jazeera from Harare.
Chinamasa said if Mugabe refused to step down, then there was no other option than the parliament to begin impeachment proceedings.
“It is a route that we don’t want to go – it will be most unfortunate if we were go down that road – but it’s the constitutional route available to parliament to remove a president from his position,” he added.
Striking a more emotional tone about the events of the past few days, Chinamasa said Mugabe has been a politician that has “shown very good leadership” over the years, but was recently taken advantage by the people close to him, including his wife.
“We have travelled with the president for decades,” he said.
“We have faced many challenges together as a party and he has provided very good leadership, and the unfortunate thing which is happening to me, when you part ways with a person you respect, who has scored many achievements for this country, for the region, for the continent and or the world, it is very hard [to see it ending this way].
“But it’s all unfortunately because of his advance in age, he became a victim to his wife and the allies of his wife who basically abused his position and directed him to do things which were not in the interest both of the party and government.”
Zimbabwe is expected to hold elections next year.
With reporting from Haru Mutasa and Tendai Marima in Harare.