A deal to release Israeli hostages in exchange for Palestinian prisoners could be finalized days before the inauguration of President Donald J. Trump. The scenario is reminiscent of 1981, when American hostages who had been held in the American embassy in Tehran for more than a year were released just as Ronald Reagan became commander-in-chief.

On January 20 of that year, Mr. Reagan, who had just been sworn in as president, told members of Congress at a luncheon after his inauguration that the 444-day hostage crisis that had blighted the last year of the administration of his predecessor, Jimmy Carter. , it was finally over. “They are free now,” said Mr. Reagan on POWs.

The hostage crisis began in the Islamic Revolution, led by Ayatollah Ruhollah Khomeini, which overthrew the Iranian monarchy in 1979. In October of that year, Mr. Carter decided to allow the exiled Shah of Iran to travel to the United States for cancer treatment, angering the Iranian revolutionaries.

The following month, Iranian militants seized the US embassy in Tehran and took 66 hostages. More than a dozen prisoners were released early, and 52 diplomats, guards and embassy employees remained in captivity.

In order to put pressure on Iran for their release, Mr. Carter stopped buying Iranian oil and froze all Iranian assets in the United States. He ordered a military rescue attempt in April 1980, but the mission failed and turned into a disaster when the helicopter crashed American plane in the Iranian desert, killing eight marines and airmen.

Anger in the United States over the prolonged detention of hostages contributed to Mr. Carter. In November 1980. Mr. Reagan prevailed in the presidential elections over Mr. Carter, who continued to work on the Iran deal during the last night of his presidency.

American negotiators, who worked day and night five days in an effort to end the crisis before he leaves office, said at the time that he did not know whether Iran was deliberately delaying the talks to ensure that Mr. Reagan would be president when the hostages were freed.

Peter Baker contributed reporting.