The New York University School of Medicine announced on Thursday that it would cover the tuition of all its students, regardless of merit or need, citing concerns about the “overwhelming financial debt” facing graduates.

N.Y.U.’s initiative comes at a time when affordability has become an increasingly urgent issue in higher education, with some graduates struggling with thousands of dollars in debt.

To date, much of the effort has centered on helping undergraduates cover the balance of their tuition bills, including at community colleges in Tennessee, and two- and four-year schools in New York under the new Excelsior Scholarship.

In the field of medicine, schools have become worried that students saddled with steep debt are increasingly pursuing top-paying specialties rather than careers in family medicine, pediatrics and research. So it was big news in December when Columbia announced a $250 million gift from Dr. P. Roy Vagelos, an alumnus who is a former chairman of Merck & Co., and his wife, Diana, that would offer students with the greatest financial need full-tuition scholarships, and other students grants, rather than loans.