Limiting the number of foreign doctors who can get visas to practice in the United States could have a significant impact on certain hospitals and states that rely on them, according to a new study.

The research, published online in the Journal of the American Medical Association this week, found that more than 2,100 U.S. employers were certified to fill nearly 10,500 physician jobs through H-1B visas nationwide, in 2016. That represents 1.4% of the physician workforce overall.

There were wide variations by state and employer, however.

Related: Hospitals, doctors in limbo after fast-track processing of H-1Bs is halted

Employers in New York, Michigan and Illinois accounted for the most H-1B visa applications for foreign physicians, nearly a third of the total. North Dakota, however, had the most applicants as a percentage of its physician workforce: 4.7%.

The top three employers that submitted applications for the most doctors through the visa program were William Beaumont Hospital in southeastern Michigan, with 470 physician applications, Bronx-Lebanon Hospital Center in New York City, with 213, and Cleveland Clinic foundation in Ohio, with 180.

"People underestimate the fragility of certain hospitals and their reliance on certain physicians for their functioning," said study co-author Peter Kahn, who's graduating from Albert Einstein College of Medicine in the Bronx this spring.

Related: Visa crackdown puts these rural doctors at risk

The H-1B visa program allows employers to hire highly skilled professionals from abroad to fill employment gaps in the U.S., typically in high-tech, science, engineering and math jobs. But hospitals use the program as well, often to recruit doctors to serve in rural or underserved urban areas. The number of visas is capped at 85,000 annually.

That could change.

On Tuesday, President Donald Trump signed an executive order reiterating his administration's priority to buy American goods and hire American workers. Among other things, it requires federal agencies to suggest reforms to the H-1B visa program to ensure the visas are awarded appropriately.