WASHINGTON — Weeks after their dramatic escape from Kabul, tens of thousands of Afghans hoping to be resettled in the United States remain on military bases across the country and overseas as medical and security screenings slow the process.

A small but worrisome measles outbreak has contributed to the delays, causing a halt in evacuation flights as federal officials scramble to contain cases and inoculate new arrivals against the disease and other illnesses, including the coronavirus.

As of Sept. 14, about 64,000 evacuees from Afghanistan had arrived in the United States. The vast majority were at risk under Taliban rule after the U.S. withdrawal from the country last month. Nearly 49,000 are living on eight domestic military bases, waiting to be resettled in the United States, according to an internal federal document obtained by The New York Times. Roughly 18,000 are on bases overseas, largely in Germany. Some leave within weeks, but most stay longer.

The screenings, which involve an array of federal agencies, follow a condensed and harried evacuation effort last month shortly before the United States completed its withdrawal from Afghanistan. About 100 Americans who want to leave, and an unknown number of vulnerable Afghans, remain in the country.

Antony J. Blinken, the secretary of state, defended the Biden administration’s evacuation operation during hours of congressional testimony this week, which included calls from Republican critics for his resignation and charges that the administration failed to adequately plan for the Afghan government’s collapse to the Taliban.

Mr. Blinken said there was no deadline for getting people out of the country and that “in the end, we completed one of the biggest airlifts in history, with 124,000 people evacuated to safety.”

While Afghan evacuees have escaped the Taliban, their lives remain in limbo, with restless children and little to do on the bases across the United States, including Fort McCoy in Wisconsin, where more than 12,700 people were being housed as of last week, and Fort Bliss in Texas, which has received more than 9,700.

“We will be here one month or more,” said Milad Darwesh, who arrived Saturday at Joint Base McGuire-Dix-Lakehurst in New Jersey after traveling for days to reach the United States. There are nearly 8,000 evacuees at the base.

Mr. Darwesh said he and his family narrowly escaped Kabul in a harrowing journey with the Taliban on their heels to the gates of the airport there. They spent four days in Doha, Qatar, along with thousands of other evacuees, with little water for drinking or washing. He and his family were then transported to an airplane hangar at a base in Italy before finally making it to Fort Dix.

“It’s nice here,” said Mr. Darwesh, a former military translator who has been waiting for two years to have his visa processed. “We now have our own room.”

Zainullah Zaki, who is traveling with his family, landed in Qatar on Aug. 18 and traveled on to Germany, where he has been told over and over again that he might be on a flight “in days.”

“Because of measles, all the flights are paused right now,” John Kirby, a Pentagon spokesman, said on Wednesday about those still on military installations overseas. “So nobody is going anywhere. But our goal has been to try and move them as quickly as possible. We know that these men and women and their families want to get on with their lives.”

Seven measles cases were discovered among Afghans at the domestic military bases. Very few evacuees have tested positive for the coronavirus, according to a Sept. 10 internal government update. Afghan nationals settling in the United States are required to have a series of vaccinations, which are being given at military bases in the United States and will soon be administered overseas as well.

Many evacuees have arrived at Dulles International Airport in Virginia, and hospitals in the state have complained to the federal government that they have been overwhelmed by Afghans in need of medical treatment. Health care providers have asked for financial assistance, and Virginia’s two senators, Mark R. Warner and Tim Kaine, both Democrats, sent a letter to Biden administration officials pushing for better coordination.

“Virginia ambulances and hospitals, already occupied with regular patient needs and dealing with the additional stress of Covid, have done superb work to partner with federal agencies managing this processing effort and make sure that emergency health needs of our Afghan partners are met,” Katie Stuntz, a spokeswoman for Mr. Kaine, said. “The health providers deserve reimbursement for this work, and Senator Kaine is working with all stakeholders to make sure that happens.”

Refugee groups have scrambled for weeks to prepare for large numbers of Afghan refugees but so far have seen only a trickle of people ready to be resettled.

“In last few weeks, we served more than 100 people,” said Krish O’Mara Vignarajah, the chief executive of Lutheran Immigration and Refugee Service, a resettlement agency that has affiliates in 22 states. “Some are coming with little more than a backpack. We know the importance of an orderly system that processes and prepares these new Afghan arrivals, helping them make informed decisions on where they ultimately want to resettle.”

Ned Price, a State Department spokesman, said on Wednesday that the administration was trying to move the evacuees off military bases “as quickly and efficiently as we can.”

“We would like to see them resettled in communities,” Mr. Price said. “So it is not in our interest, it’s not in their interest for them to reside on a U.S. military base or any other official installation for any longer than is necessary, and I think you’ll see that we’re able to administer these vital steps with a good deal of efficiency.”

U.S. military service members have been supporting Afghans at bases by raising funds and delivering items such as prenatal vitamins, nutritional supplements and clothing. Many nonprofits, including Armed Services YMCA and the Catholic Diocese of El Paso, have also been helping, but the distribution of supplies has been slow because of a dearth of personnel.

Miriam Jordan contributed reporting from Los Angeles, and Michael Crowley from Washington.