Further street protests have been called in Harare, raising fears that the political turmoil could spill into violence.
Mnangagwa, seen as the preferred candidate of the military chiefs who took power last week, said he would only return to Zimbabwe when he his safety was guaranteed and he would not face arrest.
Mnangagwa's intervention -- his first since the army seized control -- comes as lawmakers of Mugabe's once loyal ZANU-PF party were to meet in parliament at 1215 GMT to trigger proceedings that could see the president stripped of office.
The dismissal put Mugabe's wife Grace in prime position to succeed her 93-year-old husband, prompting the military to step in to block her path to the presidency.
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After Mnangagwa fled abroad, the army took over the country and placed Mugabe under house arrest -- provoking amazement and delight among many Zimbabweans as his autocratic 37-year reign appeared close to an end.
Mnangagwa -- formerly one of Mugabe's closest allies and a regime hardliner -- said in his statement that Zimbabweans had "clearly demonstrated without violence their insatiable desire" for Mugabe to resign.
On Saturday, Zimbabweans attended huge, peaceful anti- Mugabe marches that would have been brutally repressed just weeks ago.
The influential war veterans' association called for immediate protests outside Mugabe's private residence -- upping the risk of civil unrest.
"We are calling on the people of Zimbabwe to settle their scores with President Mugabe so that he leaves office immediately," war veterans' leader Chris Mutsvangwa -- another former Mugabe loyalist -- told AFP.
"We are on the hour of victory. All the people must leave what they are doing and proceed to Blue Roof (Mugabe's residence). We want to see the back of him immediately."
Chiwenga called for patience and calm after elated Zimbabweans were stunned to see the president declaring in a TV address on Sunday that he was still in power.
Mugabe is feted in parts of Africa as the continent's last surviving independence leader.
He was a key figure in the war for independence and took office as prime minister in 1980, riding a wave of goodwill.
His reputation was swiftly tarnished, however, by his authoritarian instincts, rights abuses and economic policies.