The interpreters and immigration attorneys say the denials are occurring as U.S. troop withdrawals raise concerns about Taliban reprisals, The Washington Post reported Sunday.
The State Department has turned down the interpreters' applications because it says there is no serious threat to their lives. Applicants have to prove they are "experiencing an ongoing serious threat as a consequence of employment by or on behalf of the U.S. government," said Robert Hilton, a spokesman for the U.S. Embassy in Kabul.
He did not explain what constituted a "serious threat."
One military officer, Lt. Matt Orr, expressed his frustration with the program after his interpreter, identified only as Naseri, was denied a visa.
"Every house we went into, he went into. Every firefight we went into, he went into," Orr wrote in a letter to the State Department. "I feel a real sense of frustration with the bureaucratic mess that would do something like this."
Rep. Tulsi Gabbard, D-Hawaii, a veteran of the Afghan war, said threats to the interpreters were "being downplayed or disregarded" by the State Department.
"The current process for approving visas threatens to undermine the commitment we made to stand with them," she said.
"Failing to act puts lives at further risk and hurts our credibility around the globe," said Sen. Jeanne Shaheen, D-N.H., a member of the Armed Services Committee.
Some 1,648 Afghan interpreters have been granted visas since the Special Immigrant Visas program began four years ago. Congress has allotted 8,750 visas under the program.
A similar program has granted visas to more than 6,000 Iraqis over the past five years. Immigration attorneys say only Afghans have been denied the "serious threat" visas.