WASHINGTON >> Family members of Glen Doherty, a CIA contractor and a former Navy SEAL who was among four Americans killed in the 2012 terrorist attack in Benghazi, Libya, said they felt a sense of closure when they were told last December that the agency had finally agreed to pay Doherty’s death benefits.

“It was such a great Christmas gift that all this hard work and time and energy that we put in was finally done,” said Kate Quigley, Doherty’s sister, of the family’s effort in fighting for the funds. “We felt like it was honoring his name and his legacy.”

But a year later, the Doherty family has yet to see any federal money. Bureaucratic delays continue, even as the CIA and Congress are now in agreement that paying the death benefit is the right thing to do.

The family’s fight has been overshadowed by the politics and recriminations surrounding the House Select Committee on Benghazi, whose Republican members have sharply criticized Hillary Clinton for what they say was her failure as secretary of state to secure the diplomatic compound in which Doherty and the other Americans died.

Doherty’s family members say he did not realize that the life insurance package he was legally required to buy from a private provider as a CIA contractor would not pay death benefits — beyond funeral costs — if the deceased had no spouse or offspring. Doherty was single and did not have any children.

“An injustice has been done in his name,” Quigley said in a recent telephone interview. “Seventeen years, he devoted his life to protecting this country.”

In response to the Doherty family’s efforts, the CIA has proposed changing one of its administrative policies to allow it to pay up to $400,000 in death benefits to Doherty’s family and to families of terrorist attack victims in similar situations. The change would be retroactive to April 18, 1983, when suicide bombers killed dozens of people at the U.S. Embassy in Beirut.

The proposed policy, which is modeled after one adopted by the State Department for the 2014 fiscal year, would use CIA funds rather than insurance money to pay the families, providing a stopgap for those otherwise unable to collect benefits.

After months of debating the particulars of the proposal, four congressional committees responsible for approving it have done so, but the House defense appropriations subcommittee has told the CIA it must find money for the death benefits in a different part of its budget than the agency initially proposed. The committees are now awaiting the CIA’s response, which they must all approve.

“We are involved in a little game of Ping-Pong here,” said Rep. Stephen F. Lynch, D-Mass., who has pushed for the rule change on Capitol Hill. “And I feel like we’re getting close, but I don’t want to take an eye off the ball.”

Lynch said that the rule change would most likely affect several dozen families. The CIA declined to comment.

Lynch, the ranking Democrat on the House Oversight National Security Subcommittee, introduced legislation in January to go further than the internal CIA change and update what he and others called an outmoded law. His measure would amend the 1941 Defense Base Act, which requires overseas contractors — including those working for the CIA — to carry disability and life insurance. But it allows death benefits only to surviving spouses or children.

Despite gaining the support of Sens. John McCain of Arizona and Lindsey Graham of South Carolina, both Republicans, the legislation has found little traction on Capitol Hill, which Lynch said in an interview might be because of its relatively narrow focus.

Jerry Komisar, the president of the CIA Officers Memorial Foundation, which offers financial support to the families of officers killed in the line of duty, said that the death benefit of up to $400,000, while modest, would provide a much-needed lift to families.

“The demands on CIA officers to serve on some of these hazardous assignments is going up,” said Komisar, a former member of the CIA’s clandestine service. “The more we do to help incentivize them the better.”

Over the past three years, Quigley, 42, said she has made dozens of phone calls and news media appearances, as well as trips from her home in Boston to lobby lawmakers in Washington. She has also met with members of the Benghazi committee, who she said pledged support. (Jamal Ware, a spokesman for the committee, said its chairman, Rep. Trey Gowdy, R-S.C., has worked behind the scenes to help the family.)

At one point, the family had been considering bringing a $1 million wrongful death lawsuit against the CIA and the State Department. But it decided not to press the lawsuit after the CIA agreed to the policy change. The family settled a separate lawsuit against Rutherfoord, the insurance firm that sold Doherty his policy.

Doherty, who was 42 when he died, had served in Iraq and Afghanistan and had been hired by the CIA to help with security and surveillance in Libya. According to Quigley, her brother had designated a friend, Sean Lake, as the executor of his estate and did not know he would be unable to collect and distribute insurance benefits to the family as they had planned.

“The basic impetus of this is that this young man, a former Navy SEAL, agreed to serve us in a very meaningful way, in several very dangerous theaters,” said Lynch, who does not represent the family’s home district but became involved in its efforts early on.

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