As a result, very few of the estimated 110,000 Iraqis who appear to be eligible for the refugee program have been interviewed by immigration officers or undergone other screening processes necessary before they can move to the United States, the officials said. Both spoke on the condition of anonymity to more frankly discuss an internal and politically delicate issue.

A spokesman for the United States Citizenship and Immigration Services, which conducts the interviews, said teams of refugee officers continue to travel to the Middle East, including to Iraq, to interview applicants on what are known as “circuit rides.” The spokesman would not say when the last circuit ride in Iraq had been conducted, citing security concerns.

A State Department spokeswoman said fewer high-priority Iraqi refugees had been admitted to the United States in part because of tougher background checks ordered by Mr. Trump last year. “The security checks take time, but they are critical,” she said.

Secretary of State Mike Pompeo said on Saturday that American support for refugees went beyond the immigration system, and pointed to a border crisis that warranted certain limits.

“Prioritizing the cases of those already in our country is simply a matter of common sense,” he said in a statement.

Since the 2008 fiscal year, the United States has accepted 47,331 Iraqi refugees under the Direct Access Program, giving priority in the resettlement process to those who were affiliated with the American government during the Iraq war. Of those, 3,249 were accepted during the first three years of the Trump administration, the government data show.

Initially, the Pentagon had requested that 6,000 slots be given to the high-priority Iraqi refugees for the 2020 fiscal year. But others in the Trump administration, wary of a continued threat from the Islamic State, fought to lower the number of Iraqis, viewing them as a security risk.