The W.H.O. said in May that the Olympics would not significantly affect the spread of the Zika virus and that canceling the Games did not make sense. Its assessment came after a group of health experts called for the Games to be canceled, arguing that holding them would only exacerbate what had become a global epidemic.

But the W.H.O.’s assessment appears to have been be right, health experts said Friday.

“Many people have been tested and there have been no confirmed cases,” said Dr. Peter Salama, the executive director of outbreaks and health emergencies at the agency, adding that Brazil had been on high alert with “enhanced and active surveillance.”

“We feel fairly confident that the risk assessment that there would be no significant increase of transmission due to the Olympics seems to be on track,” he said.

Scientists have known about Zika since the 1940s, but its explosive spread in Latin America began only recently. Symptoms in adults are mild, but the virus can cause severe birth defects in pregnant women, so it is being tracked closely. It moved from Brazil to Colombia and is now spreading fast in the Caribbean, particularly in Puerto Rico, where there are more than 14,000 infections, including in nearly 1,000 pregnant women. In the continental United States, small clusters have occurred in South Florida.

Experts said the world should still be on high alert. They said the disease was probably becoming endemic in a number of countries.