As the Zika virus swept north from Brazil into the Caribbean, bringing with it frightening risks for pregnant women and their unborn children, United States health officials decided in February that all expectant women who had visited the countries affected should be tested for the disease.

But after the guidelines were put in place, public health officials and doctors in New York City found that large numbers of women, many uninsured or low-income immigrants from the Caribbean and Latin America, were not being screened and tested in a systematic way.

The problems facing the city’s health care providers in ensuring that all of those who need testing can get it illustrates the monumental challenges involved in reaching those considered most at risk. And as summer approaches, the reach of mosquitoes that carry the virus is expected to extend to Florida and other states along the Gulf of Mexico.

The exact number of people missed is not known, because “nobody really keeps data on how many women who traveled to a Zika area should be tested,” said Dr. Jay Varma, deputy commissioner for disease control at the New York City Department of Health and Mental Hygiene.