Former officials of the Carter administration, describing their deal to free the American hostages as "fair and reasonable," tonight strongly urged their successors in the Reagan administration to accept the agreement as made.

With officials of the new administration still studying the agreement, former White House counsel Lloyd Cutler insisted it contains commitments that are "in the interest of the United States.

"It was the intention of the government that made them to fulfill them," he added.

Recounting the agonizing final hours of negotiations, the officials said that during that last two days of activity, phone lines were kept open between Washington, Algiers and London and that then-president Carter received last-minute reports even as he prepared to attend inaugural ceremonies for Ronald Reagan.

The last call came to Carter in an office at the Capitol as he awaited the beginning of Reagan's inauguration ceremonies, but the agreement came together too late for Carter to enjoy the achievement of the hostages' release as president.

By then, everything had been in place for more than two hours, but still the plane waited on the tarmac in Tehran while the last minutes of the Carter presidency slipped away.

"They never have done anything on time," one official said of the delay, adding that he believed it was "mostly mechanical" and not just a last attempt to embarrass Carter.

The Carter administration officials talked to reporters on the plane that brought the former president here to meet the newly freed Americans, a bittersweet journey that finally brought Carter face to face with the hostages whose fate haunted him until the final moments of his term.

From outside appearances, Carter -- now Reagan's envoy -- was still traveling in the style of a president. When his familiar blue-and-white aircraft landed in Frankfurt, several thousand Americans cheered and waved American flags to greet him.

West German Chancellor Helmut Schmidt and former secretary of state Cyrus Vance, already in West Germany to greet the returning Americans, headed the delegation that welcomed Carter at the airport.

Although Carter was already out of power, people in the crowd held several signs expressing affection for him "We still love you, Mr. Carter," said one. "You're still number one with us," read another.

Spotting the friendly faces, the former president plunged into the crowd for a round of handshaking before entering a limousine for the 30-minute drive to the hospital.

His aides, in urging that the accord be respected as it was concluded, were speaking before Reagan administration officials in Washington pledged to review it in advance of carryng out the provisions still to be implemented. But the Carter officials nevertheless seemed clearly to be defending what they had done.

They gave this version of how the negotiations unfolded:

The contacts began in early September, the officials said, after statements from Iran suggested the Iranians had concluded the hostages had become "a net liability instead of a net benefit."

One of the officials said they believe the Iranians were aiming to close the deal by Nov. 4, election day in the United States, but that "the [Iran-Iraq] war, along with their own ineptitude, lack of control and stupidity prevented that."

Initially Iran pushed hard for the United States to turn over military spare parts that were frozen along with other Iranian assests after the hostages were taken. But when Carter, around the time of his campaign debate with Reagan, publicly mentioned the spare parts issue, it caused consternation in Iran, where it was read as a potential suggestion of a renewed military relationship with the United States.

"That was political anathema and they never mentioned spare parts again," said one official, who added that Iran may still have rights to the cash value of the spare parts it had purchased before the fall of the late shah.

The negotiations progressed through the fall and into the new year until, on the weekend before Carter was to leave office, they appeared close to settlement. On Monday, a last-minute hitch, which officials blamed on an "over-drafted document with too much detail" to which the Iranians objected, was finally overcome, but the waiting was not over.

The low point for the Carter aides came between 11 p.m. Monday and 4 a.m. Tuesday while they waited for Iran's central bank to send a telex message to its firm of solicitors in London as part of the agreement.

"Those were the lowest moments," said an official in describing this waiting process until the voice of one of the lawyers in London came over the open phone line to the White House and announced: "The machine just burped."

But when the message came in, it contained a wrong code number, an error of deep concern to the bankers involved in this enormously complicated movement of billions of dollars in the night. There was more hesitation until, according to one official, "with the aide of the secretary of the Treasury, the banks took their courage in their hands and went ahead with it." t

By 9 a.m. Tuesday, everything was in place for release of the hostages. Carter was in the White House, preparing for the inaugural ceremonies, and Gary sick, a National Security Council aide, was in the situation room waiting for word from Tehran.

Every few minutes, Sick called Carter, who hoped to announce the hostages' release before he left office. He called him in the White House family quarters, in the Blue Room where the Carters and Reagans shared coffe, in the limousine that carried the president and president-elect up Pennsylvania Avenue to the Capitol, and finally in a room at the Capitol just before Reagan took the oath of office.

But still the plane waited in Tehran, waited until Reagan was president. But perhaps, given the nature of the deal that had been struck, the delays should not have been surprising. It was, said Carter aide Hamilton Jordan, "like a Willie Mascone pool shot where you have to hit the ball perfectly and if you do, 10 balls fall in the pockets at one time."