For a generation, medical schools in the Caribbean have attracted thousands of American students to their tiny island havens by promising that during their third and fourth years, the students would get crucial training in United States hospitals, especially in New York State.

But in a fierce turf battle rooted in the growing pressures on the medical profession and academia, New York State’s 16 medical schools are attacking their foreign competitors. They have begun an aggressive campaign to persuade the State Board of Regents to make it harder, if not impossible, for foreign schools to use New York hospitals as extensions of their own campuses.

The changes, if approved, could put at least some of the Caribbean schools in jeopardy, their deans said, because their small islands lack the hospitals to provide the hands-on training that a doctor needs to be licensed in the United States.

The dispute also has far-reaching implications for medical education and the licensing of physicians across the country. More than 42,000 students apply to medical schools in the United States every year, and only about 18,600 matriculate, leaving some of those who are rejected to look to foreign schools. Graduates of foreign medical schools in the Caribbean and elsewhere constitute more than a quarter of the residents in United States hospitals.