The 93-year-old was put under house arrest during a military takeover on Wednesday, amid a power struggle over who would succeed him.
There has been no official word on the outcome of talks he had with regional envoys and the army chief earlier.
But sources say he has so far refused to agree to move aside.
Opposition leader Morgan Tsvangirai said earlier it was “in the interests of the people” that Mr Mugabe “resign… immediately”.
The army moved in after Mr Mugabe last week sacked Vice-President Emmerson Mnangagwa, signalling that he favoured his wife Grace Mugabe to take over his Zanu-PF party and thus the presidency.
The BBC’s Andrew Harding, in Zimbabwe, says that if President Mugabe can be persuaded to step down officially it could help legitimise the military’s dramatic intervention.
On the streets, it is hard to find anyone who wants Mr Mugabe to stay on, our correspondent adds, but negotiating the manner of his departure and some sort of transitional agreement to follow could take some time. (Courtesy BBC)