The US Supreme Court has thrown out a lawsuit against Iran worth $33bn on behalf of Americans taken hostage during the 1979 Islamic Revolution.
The hostage crisis is still used as a symbol of Iranian independence
They were held captive at the US embassy in Tehran for 444 days in a crisis which largely cost Jimmy Carter the 1980 US presidential election.
The accords which led to their release ruled out future US legal action.
The Supreme Court did not comment on its decision but US officials have said the Algiers Accords remain in force.
Congress has passed bills allowing former hostages to pursue lawsuits in a bid to bypass the Algiers Accords and Tehran hostages filed a class action in 2000.
Last year, the US Court of Appeals for the District of Columbia Circuit ruled the accords remained in effect because Congress had not been clear enough in its actions.
The state department also called for the lawsuit to be dropped because of the legal action ban contained in the accords.
The Tehran hostages' lawyer, Harvard law professor Laurence Tribe, said Congress had sought to "provide a meaningful remedy for the terrible ordeal that the [former hostages] and their families endured".
The release of the hostages coincided with the inauguration of Ronald Reagan after he defeated Mr Carter.