“On one hand, we need more people because the economy is booming,” he said. “Then on the other hand, to say, ‘The country is full, go back’ — it’s impossible to reconcile those.”

The H-2B visa program, which started in the mid-20th century, has been a feature of a persistent debate over using foreign workers for seasonal labor.

Unions and immigration opponents argue that hiring H-2B workers suppresses wages and deprives Americans of jobs. Advocacy groups say foreign workers are often exploited, and employers say the cap encourages businesses to hire undocumented workers.

Andrea Palermo, a spokeswoman for the Department of Homeland Security, did not directly answer questions about what was behind the plan for additional H-2B visas. She also did not address questions about the apparent contradiction in the administration’s positions.

“Congress — not D.H.S. — should be responsible for determining whether the annual numerical limitations for H-2B workers set by Congress need to be modified, and by how much, and for setting parameters to ensure that enough workers are available to meet employers’ temporary needs throughout the year,” she said.

The White House did not immediately respond to requests for comment on Sunday.

Mr. Nowrasteh said he favored the H-2B program. “I think the economic benefits from the H-2B visa are very large, the benefits to the workers are huge,” he said.

Because businesses are required to show that no American workers want the jobs, the cap “makes no sense,” he said.