Of 53,000 Afghan refugees being housed on U.S. military bases, all have now been vaccinated against measles, and 84 percent have received coronavirus vaccinations, a senior military official said Thursday.

Air Force Gen. Glen D. VanHerck, who heads the U.S. Northern Command, told reporters that flights to bring about 14,000 additional Afghans whose transit to the United States was suspended due to fears of a measles epidemic would begin arriving “potentially in the next week” after clearing a 21-day post-vaccination period.

Security incidents, he said, have been minimal.

The update came as an evenly divided Senate narrowly turned back a Republican amendment that sought to curtail assistance to the relocated Afghans, and as former president Donald Trump and others in the GOP voiced concern about the vetting process.

Sen. Tom Cotton (R-Ark.) sought to attach the amendment to legislation to fund the government into early December, which passed later Thursday with bipartisan support. Cotton’s amendment received 50 votes along partisan lines, one short of the number needed to succeed.

The amendment sought to cut off housing, food and medical aid, among other assistance, as of March 31, 2023, for Afghans who were granted parole to quickly enter the United States. Cotton also sought to delete language from the spending measure that would allow recent Afghan refugees to obtain driver’s licenses or identification cards without documentation typically required.

In a statement Thursday, Trump urged fellow Republicans to vote against the larger spending legislation, arguing that the provisions affecting Afghan refugees amounted to “a major immigration rewrite” that would provide “free welfare and government-issued IDs.”

“We’ve already seen some of the horrible assaults and sex crimes that have taken place,” Trump said. “But these terrible assaults will just be the tip of the iceberg of what’s coming if this isn’t shut down. . . . This bill must be opposed.”

Republicans simultaneously have criticized the Biden administration for moving too slowly to evacuate Americans and high-risk Afghans, and for allowing “unvetted” Afghans to enter the country.

In a letter last week to President Biden, Cotton and three other Republican senators — Ted Cruz (Tex.), Ron Johnson (Wis.) and Kevin Cramer (N.D.) — referred to what they called “credible reports” of child abuse and trafficking among the arriving evacuees. They did not provide the reports.

Speaking to reporters at the Pentagon, VanHerck said that despite “various reports of law enforcement challenges” among the Afghans, there have only been a “small number of incidents.”

Two evacuees are currently in federal custody, VanHerck said, although he did not detail any charges. There have been eight reported cases of robbery and theft, he said, and the FBI is investigating an alleged assault of a female soldier last month at Fort Bliss in Texas.

“For a population of 53,000,” he said, “what we’re seeing is law enforcement violations on par with and in most cases significantly lower than in similar-sized” American towns and cities.

At the same time, he said, there are more than 600 law enforcement professionals assigned to each of the eight base task forces “every day — three to four times the average of most cities.”

VanHerck said there had been a total of 24 reported cases of measles and that “the vaccination rate . . . will be at 100 percent today.” At the same time, he said, less than one half of one percent of evacuees had tested positive for the coronavirus, and 84 percent had now received mandated vaccinations.

“The task forces’ concern is primarily flu outbreak at this point,” he said. “We’re working hard to get flu vaccine as well across all Afghans.”

VanHerck said that slightly more than 4,000 refugees have completed all medical and security screenings. Asked how many had been “pulled out” for problems during security vetting, he said he did not know the number but was unaware of “any significant problems we have had once they have arrived at any of our task forces.”

When they began arriving in late August, it was estimated the evacuees — many of whom hold Special Immigrant Visas for having aided U.S. operations in Afghanistan or are applicants already in the approval process — would stay at the military bases only a few weeks before their release into the general population.

Officials have characterized the vetting process as complicated. But VanHerck said the primary “output” problem at the moment was “relocation.”

Federal and nongovernmental agencies are “very conscious to ensure that each has a great place to land and assurances of where they are going to relocate,” VanHerck said. “I understand that right now is a limiting factor on output.”

Correction: A previous version of this article said incorrectly that one of two Afghans being held in federal custody was an evacuee who allegedly assaulted a female soldier at Fort Bliss. The FBI is investigating that case, and no related arrests have been made. The article has been corrected.