In practice, businesses say the increased red tape has made it harder to secure employment-based visas. That has added to the difficulty of finding qualified workers with the unemployment rate falling to 3.9 percent.

A recent analysis of government data by the National Foundation for American Policy, a nonpartisan research group, found that the denial rate for H-1B visa petitions for skilled foreign workers had increased 41 percent in the last three months of the 2017 fiscal year, compared with the third quarter. Government requests for additional information for applications doubled in the fourth quarter, a few months after Mr. Trump issued his order.

Experts say a sustained reduction in immigration could dampen growth over time as more baby boomers retire, leaving big gaps in the job market.

That goes for high-skilled immigrants and low-skilled workers, said Francine D. Blau, an economist at Cornell. The latter will be vital in fields like elder care and child care, as well as construction and cleaning.

“A lot of our labor-force growth comes from immigrants and their children,” Ms. Blau said. “Without them, we’d suffer the problems associated with countries with an aging population, like Japan.”

The Business Roundtable, a group of corporate leaders, recently challenged the Trump administration over changes that it says threaten the livelihoods of thousands of skilled foreign workers, and economic growth and competitiveness.

In a statement, United States Citizenship and Immigration Services said the administration was “relentlessly pursuing necessary immigration reforms that move toward a merit-based system.” It added that all petitions and applications were handled “fairly, efficiently, and effectively on a case-by-case basis.”