Several of his fellow hostages suffered psychological trauma in the years after their captivity, he said. One recently committed suicide. Families have broken apart, and with advancing age, the older members of the group are experiencing health problems.

Senator Richard Blumenthal, a Connecticut Democrat who co-sponsored the Senate bill along with a Republican colleague, Senator Johnny Isakson of Georgia, said he believed the decision to extend negotiations with Iran — and to give Iran $700 million a month in sanctions relief — should put a spotlight on the plight of the former hostages.

“As important as the amount of money is the amount of will or determination to do the right thing here,” he said. “I’m very hopeful that we can rejoin the battle for fairness to the victims of one of the most oppressive chapters in U.S.-Iran relations.”

The State Department said it was obligated to honor the legal immunity in the Algiers Accords, according to a senior official, but was working with Congress to find other ways to compensate the hostages. The official, who spoke on the condition of anonymity because of the sensitivity of the matter, said that the funds being paid to Iran as part of the nuclear talks came from restricted bank accounts overseas and “do not in any way impact on any attempts to compensate the former hostages.”

Tom Lankford, a lawyer in Alexandria, Va., for the ex-hostages and their families, said: “We’ve had supportive words from Secretary Kerry and his staff. What we’re after is exactly what other victims of state-sponsored terrorism are entitled to.”

In similar cases, Mr. Lankford said, courts have mandated that former hostages receive $10,000 for each day of their captivity; in cases where the victim is dead, spouses and children are entitled to $5,000 per day. That works out to damages of $4.4 million per hostage, or roughly $450 million for all the hostages.