“Let’s be clear, these exemptions are for individuals whom the United States does not consider threats,” said Peter Boogaard, a spokesman for the Department of Homeland Security. “Nothing in these exemptions changes the rigorous, multilayered security screening we do.”

Officials said the exemptions, which would immediately affect some 3,000 asylum applicants, had been in the works for years. They said the administration was acting under authority it was granted in a bipartisan compromise adopted in 2007 under President George W. Bush. That deal was struck by Senator Patrick J. Leahy of Vermont, the Democratic chairman of the Senate Judiciary Committee who has a keen interest in refugee issues, and John Kyl of Arizona, a Republican senator at the time.

The law, Mr. Leahy said this week, had barred needy refugees who met all the other requirements “for actions so tangential and minimal that no rational person would consider them supporters” of terrorism. He said the changes “help return our nation to its historic role as a welcoming sanctuary to the world’s most vulnerable populations.”

Melanie Nezer, a vice president at HIAS, a Jewish nonprofit agency that works with refugees worldwide, said her organization had been pressing for more than a decade for the exemptions, which apply to people who “gave a bowl of rice or a dollar or were forced to give support.”

Many thousands of the refugees who have come under antiterrorism bans are already living in the United States, Ms. Nezer said. They are fighting in immigration court to remain here after Homeland Security officials determined that the ban applied to them based on details the refugees themselves provided on applications for permanent resident green cards.

An Ethiopian woman living near Chicago was tortured by the government police, but faced a terrorism ban after she told American authorities that she had provided spices for breads at a bake sale for a dissident political group, said lawyers at the National Immigrant Justice Center who are representing her.

The chaotic situation in Syria forced administration officials to speed up their work to finish the rules, as they were facing increasing demands from allies to bring more refugees to this country. The exemptions, officials said, could help Syrians who lived in places controlled by rebels the United States is supporting, who might have provided some shelter or medicine to fighters combating President Bashar al-Assad.