Mr. Kelly responded, “For every senator or congressman who has your view, I have another who says, ‘Don’t you dare. This is about American jobs.’ ”

He added that he would probably release additional visas but did not specify when or how many. Even if he does, it would take two to four weeks for new workers to arrive because they must first pass an interview at an American consulate in their country of origin to obtain a visa.

President Trump — who uses H-2B workers in the winter at his Mar-a-Lago club in Palm Beach, Fla. — campaigned on a promise of reducing immigration and protecting American jobs. And while the H-2B, the offshoot of a temporary work visa created in 1952, has spawned less controversy than the H-1B visas for tech and other skilled workers, critics say the program displaces Americans just the same.

Unions, citing low wages, dispute employers’ assertions that they need the visas because domestic workers will not take the low-skilled jobs. In a 2015 report, the Labor Department’s inspector general expressed concern that employers were not trying hard enough to recruit Americans, as they are required to do before applying for the visas. The department has also documented cases of exploitation of foreign workers.