Should Mr. Trump move ahead with scaling back refugee resettlement, it would be the second time in as many weeks that he has used executive authority to reduce the influx of immigrants. Last week, he moved to end Deferred Action for Childhood Arrivals, or DACA, the Obama-era program that grants protection from deportation to undocumented people brought to the United States as children, in six months. But he called on Congress to enact a law to address those immigrants’ status.

One senior administration official involved in the internal debate over refugees described the move to curtail admissions as part of a broader rethinking of how the United States deals with migrants, based on the idea that it is more effective and affordable to help displaced people outside the nation’s borders than within them, given the backlog of asylum seekers and other immigrants already in the country hoping to stay.

Still, the prospect of capping refugee admissions below 50,000 has alarmed people both inside and outside the administration, given the refugee crisis unfolding around the world and the United States’ history of taking a leadership position in accepting people fleeing violence and persecution.

“When you get down to some of the numbers that are being talked about, you get down to a program of really nugatory levels,” said David Miliband, the former British foreign secretary who is president of the International Rescue Committee, said in an interview. “It’s not an exaggeration to say the very existence of refugee resettlement as a core aspect of the American story, and America’s role as a global leader in this area, is at stake.”

Mr. Miliband’s group is one of nine organizations — most of them religious groups — that work with the government to resettle refugees in the United States and are pressing for the admission of at least 75,000 refugees over the next year.

Two administration officials said those pushing for a lower number are citing the need to strengthen the process of vetting applicants for refugee status to prevent would-be terrorists from entering the country. Two others said another factor is a cold-eyed assessment of the money and resources that would be needed to resettle larger amounts of refugees at a time when federal immigration authorities already face a yearslong backlog of hundreds of thousands of asylum seekers.