Tens of thousands of Zimbabweans took to the streets on Saturday to celebrate the army’s takeover and to urge Mr Mugabe to quit, according to a BBC report.
They tore pictures of Mr Mugabe and marched to his office and residence.
The military says it will advise the public on the outcome of talks “as soon as possible”.
Nine of 10 Zanu-PF party chapters say Mr Mugabe should step down and their decision is likely to be endorsed at Sunday’s meeting of the party’s top body, the central committee.
Zimbabwe’s President Robert Mugabe is to meet army chiefs amid intense pressure for him to step down.
Mediation will be led by a Catholic priest, state TV said. Mr Mugabe has largely been confined to his house since the army took over on Wednesday.
The governing Zanu-PF party is also meeting to discuss whether to dismiss their founder and long-term leader.
The army intervened after Mr Mugabe, 93, fired his deputy Emmerson Mnangagwa.
Mr Mnangagwa’s dismissal made Mr Mugabe’s wife Grace front runner to become next president. He is likely to be reinstated as vice-president when Zanu-PF convene.
Mr Mugabe has led Zimbabwe since independence from Britain in 1980.
The BBC’s Andrew Harding in Harare says this is a watershed moment and there can be no return to power for Mr Mugabe.
Our correspondent says the situation appears to be getting out of Zanu-PF’s control and there could be a broad push to introduce a transitional government that includes the opposition.