In a live TV address, Mugabe said he would preside over the ruling party’s congress in December.
The Zanu-PF earlier sacked him as party leader, and gave him less than 24 hours to resign as president or be impeached.
His grip on power has weakened since the military intervened last week in a row over who should succeed him.
A crisis was triggered after Mugabe sacked his deputy, Emmerson Mnangagwa, two weeks ago, angering the army who saw it as an attempt to move his wife, Grace, into the position of his successor.
Earlier on Sunday, Mnangagwa was named as Zanu-PF’s new leader and candidate for the 2018 general elections.
At the same party meeting, Mugabe’s 52-year-old wife, Grace, was expelled from the party, alongside a number of other senior officials.
It is not entirely clear how Robert Mugabe can preside over Zanu-PF’s congress next month, following his dismissal as party leader.