The cases of thousands of Afghan interpreters who worked with the U.S. military and hope to relocate to the United States are in limbo because the government will soon run out of visas designated for the resettlement program, State Department officials said Thursday.

Worried about the welfare of linguists who are under threat for their affiliation with the U.S. government, State Department officials are asking Congress to allow the issuing of more visas during the remainder of the fiscal year and to extend the Special Immigrant Visa (SIV) program, which is set to expire in September.

About 6,000 applicants are in the pipeline, including about 300 whose cases have reached the final stage of the process. Congress set a cap of 3,000 visas for 2014. The State Department expects to have issued that many visas within days, well ahead of the end of the fiscal year on Sept. 30.

“We owe these people this opportunity to be out of harm’s way,” Heather A. Higginbottom, the deputy secretary of state for management and resources, said in an interview. “This program and our commitment to them is incredibly important.”

The State Department’s current predicament is to a large degree one of its own making. The visa program was beset for years by interagency debates, security concerns and bureaucratic processing delays. In the fall of 2012, for instance, the State Department had granted just 32 visas among more than 5,700 applicants for the immigration pathway, which Congress established in 2009.

Many applicants were blocked at the first step — the embassy in Kabul — where senior diplomats felt the departure of scores of educated Afghans would accelerate the country’s brain drain. Some officials also argued that the risk to interpreters was not so dire — even as they markedly tightened security for American personnel in Afghanistan.

Several cases that the embassy allowed to move forward were rejected by other government agencies as applicants who had gained the trust of the U.S. military were branded potential security threats.

“The State Department is working hard to catch up,” said Rep. Earl Blumenauer (D-Ore.), who is among the lawmakers leading an effort to extend and expand the visa program. “While it has made real progress, it is still behind after years of treating the SIV issue as a low priority.”

Secretary of State John F. Kerry demanded a thorough review of the program last year and asked his staff to find ways to streamline it.

“Some deserving people were simply falling through the cracks,” Kerry wrote in an op-ed column in the Los Angeles Times last month in which he acknowledged the program’s shortcomings.

In recent months, issuance of immigrant visas for linguists has increased dramatically. The State Department has been issuing roughly 400 linguist visas per month since the start of the year, and processing time has dropped to an average of eight months, cutting the wait time about in half.

While the initiative to extend the program has strong bilateral support, it remains unclear how quickly Congress could act to create more visas and how the resettlement of additional Afghans would be funded. Blumenauer and other champions of the program in the House and Senate are trying to build support for a stand-alone bill that would establish 1,000 new visas for the remainder of the year.

“The well of SIVs has dried up,” Blumenauer said. “Not in a month. Not in a week. Now. So any interpreters looking for relief, looking for the U.S. to honor our promise, are going to be left alone and without protection, often with a price on their head. That’s why this is so urgent.”

In addition to the short-term fix, lawmakers hope to extend the program until the end of 2015 and expand the eligibility criteria to encompass Afghans who have worked for American news media, nongovernmental organizations and certain government contractors.

Their proposed legislation would create 3,000 visa slots for fiscal 2015. Given the backlog of cases, thousands of applicants stand to be disappointed even if the program is renewed for an additional year.