A telephone call to Washington at midday last Thursday from Deputy Secretary of State Warren Christopher in Algiers was a "flashing illumination" of the breakthrough that would make negotiated release of the American hostages possible by the Carter administration, senior U.S. officials said yesterday.

Christopher had just received, through the Algerian Foreign Ministry, a new Iranian proposal calling for Tehran to repay in full its outstanding loans with American banks rather than reinstate its former commercial and financial relationships.

On the telephone to Washington, the chief of the U.S. negotiating team said that he did not have sufficient expert advice in Algiers to assess the Iranian bid fully. But he added, according to a participant in the conversation, "This is something that looks very interesting . . . a new approach that is something quite promising."

Until the Iranian initiative and the Christopher telephone call, high officials of the Carter administration were doubtful that the terms for the hostage release could be negotiated in the time allowed. As late as Tuesday morning, Jan. 13, two days before the Iranian move, Secretary of State Edmund S. Muskie told a visitor that success by Jan. 20, then just a week away, was a long shot because of the mass of detail that remained to be negotiated.

The Jan. 15 Iranian proposal cut through much of the seemingly impenetrable detail, setting a framework for quick agreement in a way that its drafters knew had a strong prospect of winning U.S. approval.

"Whoever drew it up understood how good it would be for us. It was very skillfully crafted, and very well thought through," said an official on the receiving end.

There was little doubt in the minds of the Carter administration policymaking team, then or now, that last week's Iranian proposal respresented a political decision to settle with the Carter administration as well as a technical decision about the means for doing so.

Just a month earlier, on Dec. 19, Iran had forwarded an unacceptable "final proposal" calling for $24 billion in gold, cash and other "guarantees" to be provided by the United States.

Receipt of this plan, which smacked of "ransom" in the public view and was politically and financially impossible in the official U.S. view, plunged Carter administration officials to the depths of despair.

At that point, Carter publicly described the prospects for success as "unfortunately quite dim," and other officials said privately that the prospects were virtually nil for an agreement before Carter's term was up.

What brought about the change of poistion in Tehran? And what were the impelling reasons that convinced the Iranians to offer terms for a deal within the capacity of the United States to meet?

Only preliminary answers to those questions are yet available here. Different factors are given different weights by the outgoing strategists of the Carter teams.

Muskie, in a news confernce and a brief interview, cited the following factors.

The U.S. economic sanctions, backed by those of many other nations, which "weighed increasingly heavily on Iran the longer that the hostages were held."

The Iraq-Iran war, which heavily taxed Iranian resources and demanded the greatest national effort by Iran. "Their ability to sustain their military efforts," as Muskie saw the Iranian need, was imperiled by the international isolation and other consequences of the holding of the hostages.

The "uncertainty" about the future of American policy in the new administration. Muskie used this formulation to deal with the possibility that tough statements by Ronald Reagan may have impelled Iran to settle now.

The extent of Reagan's effect on the Iranian mindset is a controversial question within the retiring administration. There is no doublt, from the immediate reaction, that Reagan's description of the Iranians as "barbarians" stung the revolutionary leadership of one of the world's oldest and proudest peoples. Nor can there be much doubt that the Iranians deliberately chose the settle with Carter rather than to wait for Reagan.

An independent Iranian scholar, who asked not to be quoted by name, expressed the belief that Iranians feared that Reagan would "do terrbile things" to Rian. He made the point that the United States is given credit in the Persian mind for powerful machinations, citing the very widespread belief in Tehran that the United States is the mastermind of Iraq's war effort against Iran.

Former president Richard M. Nixon, a practitioner of the diplomacy of military threats and military actions, said in an interview with WABC-TV yesterday that Iran's decision to settle now is "a classic case" of "the policy of the carrot and the stick." He added that President Carter offered them a carrot and President Reagan offered them a stick."

A senior official of the outgoing Carter administration, while not agreeing that fear of Reagan was a major factor, also said that "we probably would not be getting the hostages out now if Carter had been relected." In part, he suggested, this is because the end of the Carter administration provided a deadline that made it both necessary and posssible for the fractious Iranian power structure to make a real decision.

Muskie said in his news conference that the history of the negotiations on the hostages was "a pretty straight line" from Ayatollah Ruhollah Khomeini's four conditions for release of the Americans, announced by the Iranian leader on Sept. 12. Muskie said the United States sought to probe the seriousness of these conditions via Iranians "who were not ultimately the decision makers" but who were in a position to evaluate Khomeini's meaning.

Muskie appeared to be referring to a highly secretive trip to Bonn by Christopher and top aides less than a week after Khomeini's speech, a trip during which the Americans met a still undisclosed Iranian figure.

Whatever the validity of Muskie's "straight-line" view of the negotiations, it is clear that the major points of Iranian initiative were timed for maximum effect in the United States.

The Nov. 2 decision on the terms for release by the Iranian parliament, or Majlis, a senior official pointed out, came on the very eve of the U.S. presidential election.

"The Iranians thought Carter would be vulnerable [to domestic political pressures in the United States] at that time and would have to accept," the official said.

Muskie, in a separate interview, cited this as an example of the lack of realism of the Iranian leadership about the United States: "They were astounded that Carter wasn't reelected when the Majlis acted on their proposal. They don't understand us. They judge us by petty standards."

The next Iranian push came with their Dec. 19 proposal for $24 billion in guarantees. It was the first complete and detailed proposal submitted by Tehran, and contained many elements of the ultimate solution. But the "guarantee" feature made it unacceptable.

A U.S. policymaker noted that, once again, the proposal was made a time when the Iranian leaders felt that Carter would be vulnerable at home, just before the hostages' second Christmas in Tehran.

The third full-scale Iranian proposal, embodied in the message received by Christopher last Thursday, was, from the U.S. viewpoint, both an alteration and a compromise in Tehran's position. But there is some indication that the final bid was sold as a hard-line anti-American proposal by its authors in the Iranian capital.

The U.S. plan for dealing with the problem of old loans to Iran by U.S. banks was that Tehran reestablish them by paying past-due installments, thus restoring relations with the banks had been in secret negotiations on this point for many weeks with lawyers representing Iran, but these discussions were progressing far too slowly to bring a resolution by Jan. 20.

The Jan. 15 Iranian proposal, presented to the United States on the eve of the Jan. 16 deadline for decision set by the Carter administration, called for Tehran to pay off its old loans and completely sever its relations with the American banks.

Muskie said yesterday that, in addition to being more workable and bringing a potentially quick solution, the new proposal served the "paranoia" of Iranian hardliners by cutting off the ties with "the Great Satan."

Tehran would receive less cash under this proposal, but it did more for that nation's fierce pride and xenophobia. And, though a grueling end game of haggling and hitches was yet to come, it permitted a deal that brought 52 Americans to freedom on the last day of the Carter administration. b