Acknowledging criticism against him from the Zanu-Pf, the military and public, Mugabe stressed the need to return Zimbabwe to normalcy.
In a live TV address, Mugabe said he would preside over the ruling party's congress in December 2018.
Mugabe had earlier been sacked by Zanu-PF as party leader, and gave him less than 24 hours to resign as president or be impeached.
"The (ruling Zanu-PF) party congress is due in a few weeks and I will preside over its processes," President Mugabe said in his speech.
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"Whatever the pros and cons of how they (the army) went about their operation, I, as commander-in-chief, do acknowledge their concerns," he said.
The Zimbabwean President's grip on power has weakened since the military intervened on Wednesday, in a row over who should succeed him.
The crisis in his governance was triggered he 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, Mr Mugabe's 52-year-old wife, Grace, was expelled from the party, alongside a number of other senior officials.
