WASHINGTON — For almost two years, the family of Glen Doherty, a C.I.A. contractor and former Navy SEAL who was among four Americans killed in the 2012 terrorist attack in Benghazi, Libya, has fought to claim the government death benefits they believe Mr. Doherty deserved.

On Monday, the C.I.A. informed the Doherty family and others like them that their wait would end.

The agency has secured funds to begin paying out death benefits of up to $400,000 each to families like the Dohertys who are survivors of unmarried and childless federal employees or contractors killed in acts of terrorism overseas.

The measure circumvents a 1941 law that requires overseas contractors — including those working for the C.I.A. — to carry disability and life insurance but pays out death benefits only to those with surviving spouses or children.

Kate Quigley, Mr. Doherty’s sister who led the family’s lobbying efforts, said her brother, who had no spouse or children, did not know that his life insurance package would not pay any death benefits.