RIO DE JANEIRO — With about 500,000 people expected to visit Brazil for the Olympics here this year, researchers are scrambling to figure how much of a risk the Games might pose in spreading the Zika virus around the world.

Infectious disease specialists are particularly focused on the potential for Zika to spread to the United States. As many as 200,000 Americans are expected to travel to Rio de Janeiro for the Olympics in August. When they return to the Northern Hemisphere and its summer heat, far more mosquitoes will be around to potentially transmit the virus in the United States.

Brazilian researchers say they believe that Zika, which has been linked to severe birth defects, came to their country during another major sports event — the 2014 World Cup — when hundreds of thousands of visitors flowed into Brazil. Virus trackers here say that the strain raging in Brazil probably came from Polynesia, where an outbreak was rattling small islands around the Pacific.

As many as 1.5 million people are believed to have contracted the virus in Brazil since then, and the authorities are now investigating thousands of reported cases of babies being born recently with brain damage and abnormally small heads. Zika has spread to more than 20 nations and territories in the Western Hemisphere, according to the World Health Organization, illustrating how quickly the epidemic can expand even without a big international gathering.

By itself, the virus is not normally life-threatening, and most people who become infected have no symptoms at all.

The big question is whether Zika is responsible for the huge increase in birth defects reported by doctors, hospitals and other medical officials in Brazil over the last few months. That connection has still not been proved.

“There is more and more concern that there may be a causal relationship, but a lot of the work so far is to rule out other possible causes,” Dr. Bruce Aylward, an assistant director general at the World Health Organization, said on Thursday, adding that it might take six to nine months to know for sure.

Asked whether the W.H.O. would advise people not to travel to Brazil for the Olympics, he replied: “I would think that would be very, very unlikely.”