While 13,255 refugees were admitted in August, that number plunged to just 2,070 in March. So far during the 2017 fiscal year, 45,732 people have been admitted, just a few thousand short of Mr. Trump's proposed cap.

Refugee groups now predict that entries into the United States could increase so rapidly that the total number of refugees admitted by Sept. 30, the end of the fiscal year, could exceed 70,000. That is well below the 84,994 refugees admitted in fiscal year 2016, but not by nearly as much as many advocates had feared.

Refugee advocates were delighted by the State Department's decision.

"This is long overdue, but we're very happy," said Mark Hetfield, president and chief executive of HIAS, an immigrant aid society.

But many of the advocates said they were worried that any reprieve would be temporary.

"The president's proposed budget cuts for 2018 would mean we would have a much smaller program next year no matter what happens with his executive orders," said Erol Kekic, executive director of the immigration and refugee program at Church World Service.

Perhaps even more worrisome, refugee advocates said they had seen a slowdown in security screenings by the Department of Homeland Security, whose checks are required for refugees to enter the United States.

Still, even Republicans in Congress have said that few of Mr. Trump's proposed budget cuts to foreign aid and the State Department's budget would be adopted into law.

In a visit this week to Syrian refugee camps in Turkey, Nikki R. Haley, the United Nations ambassador, all but urged Congress to reverse Mr. Trump's proposed cuts in aid to refugees.

"It's starting the conversation," Ms. Haley said of Mr. Trump's proposed budget, according to The Associated Press. "It doesn't mean that's where it will end up. He's going to have that conversation with Congress on where we should fall on this."