"The (ruling ZANU-PF) party congress is due in a few weeks and I will preside over its processes," Mugabe said, pitching the country into further uncertainty.
Many Zimbabweans expected Mugabe to resign after the army seized power last week.
But Mugabe delivered his speech alongside the uniformed generals who were behind the military intervention.
In his address, Mugabe made no reference to the clamour for him to resign.
Instead he paid tribute to three pillars of power in Zimbabwe -- the military, the ruling party and the war veterans movement -- and urged national solidarity.
"Whatever the pros and cons of how they (the army) went about their operation, I, as commander-in-chief, do acknowledge their concerns," said Mugabe.
"We must learn to forgive and resolve contradictions real or perceived in a comradely Zimbabwean spirit," he said.
His address provoked immediate anger.
"That speech has nothing to do with realities. We will go for impeachment and we are calling people back to the streets," Chris Mutsvangwa, head of the influential war veterans' association, told AFP.
On Saturday, in scenes of public elation not seen since Zimbabwe's independence in 1980, huge crowds marched and sang their way through Harare and other cities, believing Mugabe was about to step down.
The ruling ZANU-PF party sacked Mugabe as its leader earlier on Sunday and told him to resign as head of state, naming ousted vice president Emmerson Mnangagwa as the new party chief.
Analysts say the military stepped in last week after Mugabe's wife Grace, 52, secured prime position to succeed him as president following a bitter power struggle with Mnangagwa, who has close ties to the army.
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