Mugabe's spokesman later said his much-criticized remark was misunderstood, state media reported Friday.
Friday's Herald newspaper quoted Mugabe's spokesman George Charamaba as saying Mugabe had been sarcastic and wanted to make the point that the crisis was contained.
Mugabe's comments Thursday drew strong criticism from the United States and Britain; the U.S. ambassador to Zimbabwe said it showed "how out of touch he is with the reality" in Zimbabwe.
The United Nations, though, said Friday that the death toll from the waterborne disease had risen to 792 and that the number of cases had increased to 16,700.
U.N. Secretary-General Ban Ki-moon said that he "cannot agree" with Mugabe's assessment that the epidemic has ended.
Cholera has spread rapidly in the southern African nation because of the country's crumbling health care system and the lack of clean water. The U.N. said 16,403 cases have been reported.
Just last week,declared a national health emergency due to the cholera outbreak and the collapse of its health services.
At a state funeral Thursday for a ruling party official, Mugabe insisted the outbreak of the waterborne disease had been "arrested" with the help of the World Health Organization and other aid agencies.
Mugabe lashed out at critics who have been calling for his ouster - and even military intervention - as concerns about Zimbabwe's deepening humanitarian crisis mounted.
"So now that there is no cholera, there is no cause for war anymore. We need doctors, not soldiers," he said during an hour-long address broadcast live on state television.
Mugabe has ruled his country since its 1980 independence from Britain and has refused to leave office following disputed elections in March. A power-sharing deal worked out in September with the opposition has been deadlocked over how to divide up Cabinet posts.
His latest rosy assessment of the cholera outbreak was in stark contrast to statements by health officials in the region.
"We have a cholera challenge and it's of a massive magnitude in Zimbabwe," said Thami Mseleku, a senior health official in neighboring South Africa. "There have been challenges of cholera in Zimbabwe, like every other country, and they have been able to manage them. This one is of a magnitude that is unprecedented."
President Bush, British Prime Minister Gordon Brown and French President Nicolas Sarkozy all have called recently for the 84-year-old leader to step down.
"I don't know what world he is living in," Malloch-Brown said during a one-day trip to South Africa, where he visited a Johannesburg church housing 1,600 Zimbabweans who have fled the economic meltdown.
"There is a raging humanitarian crisis in Zimbabwe as well as an economic crisis and still there is no representative government able to lead the country out of this disaster," he said.
Malloch-Brown called on South Africa to put more pressure on Mugabe to end the political and humanitarian crisis. South Africa has withheld $30 million in aid for Zimbabwe but otherwise has been reluctant to use its huge economic and political muscle against its neighbor.
"South Africa could do a lot more and it needs to do it now," said Malloch-Brown, who also met South African Health Minister Barbara Hogan, who is trying to contain the spread of cholera from across the border. He was also due to meet President Kgalema Motlanthe.
South African authorities have declared an area along the cholera-hit border with Zimbabwe a disaster as the disease spreads to other countries in the region.
About 664 people have been treated for the waterborne disease and at least eight people have died in South Africa. Hundreds of Zimbabweans cross the border at Beitbridge every day to search for jobs in South Africa, buy supplies and increasingly seek medical treatment.
Phandu Skelemani, foreign minister of neighboring Botswana, which has been critical of Mugabe, said his country's border with Zimbabwe should remain open but he supported other measures to isolate Mugabe and his ZANU-PF party.
"If you switch off petrol (gasoline), I think that ZANU-PF will have to go. If that step is agreed and you then simultaneously airlift critical supplies like food and essential supplies to prevent Zimbabweans from starving to death, I think it will have desired effect," Skelemani told The Associated Press on Thursday.
Meanwhile, France said authorities in Zimbabwe have refused visas to six French envoys who were to provide humanitarian assistance with the cholera outbreak.