WASHINGTON — The White House is considering a plan that would effectively bar refugees from most parts of the world from resettling in the United States by cutting back the decades-old program that admits tens of thousands of people each year who are fleeing war, persecution and famine, according to current and former administration officials.

In meetings over the past several weeks, one top administration official has proposed zeroing out the program altogether, while leaving the president with the ability to admit refugees in an emergency. Another option that top officials are weighing would cut refugee admissions by half or more, to 10,000 to 15,000 people, but reserve most of those spots for refugees from a few handpicked countries or groups with special status, such as Iraqis and Afghans who work alongside American troops, diplomats and intelligence operatives abroad.

Both options would all but end the United States’ status as a leader in accepting refugees from around the world.

The issue is expected to come to a head on Tuesday, when the White House plans to convene a high-level meeting in the Situation Room to discuss at what number Mr. Trump should set the annual, presidentially determined ceiling on refugee admissions for the coming year.