In rare cases, the virus has been associated with Guillain-Barré syndrome, a disorder in which the body’s immune system attacks part of the peripheral nervous system, which can lead to paralysis, usually temporary. In New York City, two people who tested positive for Zika had Guillain-Barré. They have both since recovered, Dr. Bassett said.

There is also a growing concern about the risk of sexual transmission. While all the cases in the city are believed to be travel-related, at least two other cases in New York State are thought to be the result of sexual transmission, health officials said.

Under guidelines issued in February, all women who are pregnant or trying to become pregnant and who have also traveled to Zika-affected countries should be tested, even those with no symptoms.

During the first few months after the guidelines changed, however, many of the women considered most at risk were not being tested. Dr. Bassett said that once the city recognized the problem, health officials moved aggressively to inform communities with close ties to the affected areas.

“We are seeing the disparity close,” she said on Wednesday.

Several explanations have been offered for why such a large percentage of positive tests involve travel to the Dominican Republic, health officials said.

In recent years, Dominicans have overtaken Puerto Ricans as the largest Latino community in the city, with 747,473 Dominicans living in the five boroughs in 2013, compared with 719,444 Puerto Ricans, according to the most recent census data.

And as recent immigrants, Dominicans have a greater inclination to travel between their home country and New York than other immigrant groups do.