He said there was no one with his political stature who could immediately take over from him.
The 93-year-old leader has been in charge in the former British colony since independence in 1980.
His health is closely watched by Zimbabweans, who fear the country could face chaos if he dies without anointing a successor.
Mugabe told tens of thousands of supporters at a rally in the town of Chinhoyi, in his home province, that doctors were recently surprised by his “strong bone system.”
He has travelled to Singapore three times this year for what officials said is routine medical treatment.
“There is the issue that the president is going. I am not going,” Reuters quoted Mugabe as saying to supporters on the grounds of a local university, 100 km (60 miles) west of the capital Harare.
“The president is dying. I am not dying. I will have an ailment here and there but bodywise, all my internal organs are very firm, very strong.”
Mugabe, who looks frail, had walked onto the stage slowly but without assistance.
The issue of who will succeed the veteran Zimbabwean leader has deeply divided the ruling party, with two factions supporting Vice President Emmerson Mnangagwa and Mugabe’s wife, Grace.
Grace had on Thursday challenged Mugabe to name his preferred successor, to end divisions over the future leadership of ZANU-PF.
She repeated the call on Saturday, adding that Mugabe would lead the process to choose his eventual successor.