“We are looking at the entire program to ensure the entire thing is administered well and in conformity with congressional intent,” he said.

He recently met with a group of displaced American workers in Florida, including some laid off by Disney. The meeting was arranged by Sara Blackwell, an employment lawyer who leads a group called Protect U.S. Workers. “The administration has done much more for American workers, but I hope to see much more soon,” Ms. Blackwell said.

Immigration lawyers and companies seeking the visas say that some of the decisions appear arbitrary.

After responding to requests for evidence, a consulting firm that applied for an H-1B for an energy expert from Britain received a denial stating that the skills for the position “do not appear to be of such complexity, uniqueness or specialization as to require the attainment of a bachelor’s degree,” a prerequisite for the visa.

Kristen Albertson, the operations manager at the firm, called the outcome “egregious.”

“We apply only when it’s a strong case and essential to our business,” she said of the applicant, who is a graduate of the University of Chicago.

An H-1B visa for an Indian scientist recruited by the Cleveland Clinic for his expertise in cellular biology is stuck in “administrative processing” in New Delhi, meaning it is undergoing further review that could stretch into months. “His team’s projects are now on hold due to the delay,” said Janice Bianco, an official at the Cleveland Clinic who handles applications for foreigners.

She said a visa for a pediatric geneticist hired in the spring took three months to be issued — in the past, it would have taken about three weeks — forcing the hospital to reroute some patients to other facilities.