“I am doing this because it’s the best way to keep our veterans safe, full stop,” Denis McDonough, the secretary of veterans affairs, said in a telephone interview on Monday. The department is one of the largest federal employers and is the biggest integrated health care system in the country.

The mandate will apply to workers who are “the most patient-facing,” Mr. McDonough said, including doctors, dentists, registered nurses, physician assistant and some specialists. Beginning on Wednesday, those health care workers will have eight weeks to get fully vaccinated or face penalties including possible removal, he said.

Jen Psaki, the White House press secretary, reiterated the Biden administration’s position on Friday that mandating vaccinations was a decision for the private sector companies and local communities. But the decision at the department reflects a growing consensus among private sector employers, health care centers, and state and local governments to test the legal waters on vaccine requirements as cases rise sharply around the nation.