Mugabe has been in military custody and there is no sign of the recently fired deputy Emmerson Mnangagwa, who fled the country last week.
The military remains in the streets of the capital, Harare, as the mood is tense.
Regional officials are meeting on the crisis as civil society groups and churches in Zimbabwe issue appeals for calm.
A joint statement by more than 100 civil society groups urges Mugabe, the world's oldest head of state, to peacefully step aside and asks the military to quickly restore order and respect the constitution.
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