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 had been reported.
Last week, Zimbabwe declared a health emergency because of cholera and the collapse of its health services.
At a state funeral Thursday for a ruling party official, Mugabe insisted the outbreak was under control with the help of the World Health Organization and other agencies.
"Now there is no cholera, there is no need for war," he said. "We need doctors, not soldiers."
Mugabe insisted Thursday that cholera was common in the region and that "the cholera came from other countries." However, there is growing concern about the spread of the disease to Zimbabwe's neighbors.
South African authorities said they have declared the Vhembe border area a disaster. The Limpopo provincial government's spokesman Mogale Nchabeleng said authorities would be able to mobilize resources more quickly and be eligible to receive national funds as a result of the declaration.
About 664 people have been treated for the waterborne disease and at least eight people have died. Hundreds of people cross the border at Beitbridge every day to search for jobs in South Africa, buy supplies and increasingly for medical treatment.
Mugabe, 84, has come under increasing pressure as concern about the country's deepening humanitarian and political crisis mounts. President George W. Bush, British Prime Minister Gordon Brown and French President Nicolas Sarkozy all have called recently for Mugabe to step down.
He 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.
The government acknowledges that political impasse has paralyzed public services, including health and education, amid a deepening economic collapse and runaway inflation.
The collapse of garbage collection has led to infestations of flies, insects and rats across Zimbabwe's capital.
During Mugabe's hour-long address, broadcast live on state television, flies buzzed around his podium and he picked his fingernails in agitation using a paperclip from his prepared notes.
Mugabe described Brown and Bush as "crooks" who are "guilty of deliberate lies in order to commit acts of aggression.
"We are hearing words from the white lips of regimes with a cruel history of imperialism and the blatant dehumanization of our people," he said.
"We don't like it. We don't want that prostitution in politics. Let's settle things here," Mugabe told mourners at Heroes Acre, a burial shrine for loyalist politicians and guerrilla leaders who died in the bush war that swept him to power after independence.
Tsvangirai, head of the Movement for Democratic Change, won the first round of polling on March that forced a runoff in June. But he withdrew because of state-sponsored violence against his supporters.
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