Zika virus has already been linked to brain damage in babies and paralysis in adults. Now scientists are facing another ominous possibility: that on rare occasions, the virus might be transmitted through sex.

The evidence is very slim; only a couple of cases have been described in medical literature. But a few experts feel the prospect is disturbing enough that federal health officials should inform all travelers, not just pregnant women, of the potential danger.

Officials at the Centers for Disease Control and Prevention, however, say the evidence is insufficient to warrant such a warning. While the two instances suggest a “theoretical risk” of sexual transmission, they note the primary vector is clearly mosquitoes.

Dr. Márcio Nehab, a pediatrician and infectious disease specialist at Fiocruz, a research institute in Rio de Janeiro, said that much more research was needed to be done to definitively prove that Zika can be transmitted during sex.

“At the moment we need to be more concerned with the mosquito, the vector known for transmitting the virus,” Nehab said in an information bulletin about Zika geared toward women and children.

At the moment, experts know of just one case in the medical literature of live Zika virus being detected in a man’s semen.

The man was an unidentified 44-year-old Tahitian man, exposed during an outbreak of Zika virus in French Polynesia in 2013. French scientists helping to investigate found high levels of the virus in semen samples taken from the patient, even after it disappeared from his blood.

It was unclear how long the virus had persisted in his body: He had had two episodes of fever that might have been caused by the Zika virus, one shortly before he was tested and another about two months earlier. The virus was also found in his urine.

A more unusual episode — the first clue that Zika could be sexually transmitted — occurred in 2008.

Brian D. Foy, a biologist specializing in insect-borne diseases at Colorado State University, was in rural Senegal with a graduate student, Kevin C. Kobylinski, collecting mosquitoes for a malaria study. Both were bitten many times.

About a week after they flew back to Colorado, Foy and Kobylinski each fell ill with rashes, fatigue and headaches, symptoms typical of several mosquito-borne illnesses.

A few days later, Foy’s wife — Joy L. Chilson Foy, a nurse and mother of four — showed similar symptoms, slowly developing a rash worse than that of either man, along with greater headache pain and bloodshot eyes.

All three eventually recovered. Late in his illness, however, Brian Foy had genital pain and what appeared to be blood in his semen.

Blood was drawn from all three patients and tested for the usual West African suspects: malaria, dengue and yellow fever. All were negative.

Their infection remained a mystery until a year later, when Kobylinski, back in Senegal, met another scientist who suggested it could be Zika virus. The blood samples — which Foy had frozen — tested positive. That left the question of how his wife had been infected.

She had not left northern Colorado, which has none of the mosquitoes that transmit Zika. And it seemed unlikely that she and her husband had been bitten by the same mosquito: The virus needs more than four days to move from the insect’s gut to its salivary glands.

Neither had passed the disease to their children, so even close family contact seemed noninfectious. The most likely explanation, the couple realized, was that they had had sex shortly after Foy’s return, before he fell ill.

Foy wrote about his experience in 2011 in the journal Emerging Infectious Diseases.

In an interview, Foy said he had been trying to get research money to study the phenomenon, but there have been obstacles: Until the last few weeks, there has been little interest in the obscure virus.

And Zika virus is hard to study, because it does not infect mice, rats or most other lab animals. It does infect monkeys, but that research is difficult, expensive and controversial. Colorado State does not have a monkey research colony, Foy said.

Dr. William Schaffner, chief of preventive medicine at Vanderbilt University Medical School, said it was imperative that research on possible sexual transmission of Zika be done in Brazil or another Latin American country experiencing an outbreak.

Two suspect cases “are not really enough to warrant a large public health recommendation from the CDC,” he said. “But it’s provocative, so someone else could recommend it. And it certainly should be studied.”

Testing men for the virus in their semen should be easy, he added. After that, researchers should look for couples like the Foys, in which one partner had been in a mosquito-infested area and the other had been in a mosquito-free one.

“If I was a man and I got Zika symptoms, I’d wait a couple of months before having unprotected sex,” said Scott Weaver, director of the Institute for Human Infections and Immunity at the University of Texas Medical Branch in Galveston and an expert on the virus. “If my wife was of childbearing age, I’d want to use protection, certainly for a few weeks.”

A spokeswoman for Brazil’s Health Ministry said studies about how Zika can be contracted need to be evaluated more closely. “These analyses need to be accompanied by scientific work so the Health Ministry can provide the population with safe advice about transmission of the virus,” the statement said.

On Monday, the Pan American Health Organization warned that Zika virus is likely to spread to every country in the Americas except Canada and Chile.

In the United States, CDC experts have said they expect the disease to follow the same pattern as dengue: limited outbreaks in hot, wet regions including Florida and other states along the Gulf Coast and Hawaii, where the yellow fever mosquito, Aedes aegypti, is common. They hope that aggressive mosquito control will contain the infection.