WASHINGTON - The Supreme Court on Tuesday rejected the last legal appeal for former US hostages seeking compensation for their captivity in Iran three decades ago, leaving legislation newly introduced in Congress as the last chance to resolve their longstanding grievance.

A lower court, acting at the request of the State Department, previously blocked the hostages’ effort to win compensation from Iran, holding that the agreement under which they were released barred such claims.

The former hostages had sued under a 1996 law that they argued allowed them to seek damages, and in August 2001 they won a judgment of liability, because Iran did not appear in court to defend itself. But the State Department argued that its ability to conduct foreign policy would be compromised if damages were awarded.

The Supreme Court, as is its custom, did not give a reason for its decision Tuesday.

Fifty-two Americans were held hostage for 444 days after Iranian radicals seized the US Embassy in Tehran in 1979.

“I would never have thought when I was getting kicked around in Iran that my own government would ever go to court to stop me,’’ said David M. Roeder, a retired Air Force colonel who was the named plaintiff in the case.

But after 12 years of legal wrangling, he said, he was not surprised by the outcome.

The approximately 100 plaintiffs named in the suit, which included former hostages and some of their survivors, were seeking $10,000 a day, or $4.4 million each.

According to their lawyers, money that was deposited in the United States by Shah Mohammad Reza Pahlavi of Iran before he was forced from power - funds frozen by the Carter administration after the hostages were taken - is still available.