The President spoke at a graduation ceremony in Harare amid political turmoil over the likely end of his 37-year rule.
Mr Mugabe was taken into military custody this week in what the Zimbabwean army described as a "bloodless correction".
The 93-year-old has insisted he remains in charge but looks almost certain to be forced from office if he refuses to step down, with his ruling Zanu-PF party stating there "is no going back".
Senior party figures were set to meet on Friday to draft a resolution to dismiss Mr Mugabe and lay the ground for his impeachment if he refuses to stand down.
"If he becomes stubborn, we will arrange for him to be fired on Sunday," a senior party source said. "When that is done, it's impeachment on Tuesday."
Witnesses reported seeing a helicopter hover over the Presidential motorcade as it moving through the capital on Friday, taking Mr Mugabe to a graduation ceremony at Zimbabwe Open University.
A red carpet had been laid out for Mr Mugabe as he took up his traditional role of greeting students as they collect their graduation caps.
One witness said the audience cheered as he began speaking, wearing a blue and yellow academic gown and mortar board hat as she sat in a large wooden chair at the front of the university hall.
There was no sign of his wife Grace Mugabe, whose whereabouts are unclear.
Mr Mugabe had been in military custody, reportedly with his wife, since the military takeover on Tuesday night.
On Thursday he held talks with army chiefs and envoys from South Africa about his future.
His appearance that graduation ceremony came as the military announced "significant progress" on talks for his departure and the arrest of some of his allies.
South African President Jacob Zuma, speaking in his country's parliament, said the political situation "very shortly will be becoming clear."
Seizing on the political limbo to speak out, Zimbabwean civil society groups and opposition leaders urged Mr Mugabe - the country's only leader since independence - to step aside after 37 years in power and for the country to transition into free and fair elections.
There was no sign of former vice-president Emmerson Mnangagwa, whose sacking last week angered supporters and led to the military takeover.
Mr Mugabe rejected a proposal under which he would step down allowing Mr Mnangagwa, nicknamed "The Crocodile" and a bitter opponent of Grace Mugabe, to take over temporarily until elections due to be held next year.
The President, described as angry and embittered, insisted he remains the legitimate head of state and has asked for guarantees if he were to leave sometime in the future. He is said to have demanded that there would be immunity from prosecution for his 52-year-old wife and other members of his family.
“Grace Mugabe belongs in prison: her only contribution to Zimbabwe has been to be the centre of scandals," declared Joshua Nhamburu, as his companions, fellow veterans of the war which freed the country from white rule, shook their heads in agreement. "She must face a court for what she has done. We have waited very long for justice and the time for that has come now."
Anger towards ‘Gucci Grace’ and ‘DisGrace’, as she has been called by her many critics for her profligate spending on luxuries as the country turned into an economic basket case, is just one ingredient of the passions simmering in Zimbabwe as the reign of Africa’s longest serving head of state comes to an end.
The President’s opponents, the politicians and the military who have now taken over, have taken pleasure in declaring that it took just 36 hours to end 37 years of Robert Mugabe’s grip on power.
Mr Mugabe, his wife and some of their most senior supporters were placed under house arrest at the palatial presidential residence, Blue Roof, with others were incarcerated in army barracks.
Whether General Constantino Chiwenga, the head of the military and his high command, who have taken over the country, would agree to the President’s demand to spare his wife from prosecution remains unclear. There are growing calls for charges to be made against Ms Mugabe and her cohort for alleged embezzlement and abuse - charges Ms Mugabe has denied.
Ms Mugabe's rapid political rise alarmed many who feared she could succeed her husband after he fired his long-time deputy, Mr Mnangagwa.
Among those detained was Kudzai Chipenga, Youth Wing chief, who had vowed that his cadres would mobilise to "fight and die" if necessary to defend the President and his wife against a coup. He was held at the same military base as finance minister Ignatius Chombo, another Grace Mugabe favourite, who has faced accusations of corruption.
Not all attempts at arrests were peaceful. The home of Mr Chombo in the affluent suburb of Borrowdale was pitted in bullet holes, with the front door blown in. One of his bodyguards was killed in a firefight, according to neighbours. Mr Moyo’s home also showed signs of damage caused by explosives as did that of Saviour Kasukuwere, a former Zanu PF youth leader nicknamed ‘Tyson’. Mr Moyo and Mr Kasukuwere evaded capture, fleeing to seek refuge with the Mugabes in Blue Roof.
Army troops and armoured vehicles continued to patrol the capital, Harare, on Friday as Zimbabweans went about their daily business. Residents said they had feared at first when the military moved in but praised the current calm.
Headlines in some local newspapers declared the Mugabe reign over. "Dawn of a new era," boomed one. "Mugabe remembered for brutal 37-year rule," said another.
Across the country, Zimbabweans long frustrated by crackdowns on dissent and a collapsing economy were enjoying freedoms they had not in years. For once, they did not have to contend with bribe-seeking police officers who mounted roadblocks every few miles.
Soldiers manning the few checkpoints leading into downtown Harare greeted motorists with a smile, searching cars without hostilities and wishing motorists a safe journey. Street vendors who endured police raids after Mr Mugabe ordered their removal were working without hassles. Trade unions urged workers to go about their business.
But the ongoing political crisis has led to deep concern in neighbouring states and the African Union. South Africa’s defence and state security ministers, Nosiviwe Maphisa–Nqakula and Bongani Bongo were dispatched to mediate between the imprisoned President and the armed forces. The Catholic Church delegated a priest, Father Fidelis Mukonori, who is close to Mr Mugabe, to act as an intermediary.
Alpha Conde, the Guinea President, the current head of the African Union, said that what has happened in Zimbabwe appears to be a military coup, something the army adamantly opposed. He and Angolan leader, Joao Lourenco are being kept appraised of plans to end the confrontation. Britain, the former colonial power of what was Rhodesia, and a strong critic of Mr Mugabe, has called for calm.
Cabinet ministers from four countries in the 15-nation Southern African Development Community have called for an emergency summit to discuss the political turmoil in Zimbabwe, and is also expected to talk about potential terms of Mr Mugabe's exit.
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