Despite cautious public statements and a White House warning against being "overly optimistic," Carter administration officials said yesterday the 13-month-old effort to free the American hostages appears to have reached a turning point on the basis of the latest statments from Iran.

It was clear from public statements and private gleanings reaching Washington that Iranian authorities have decided on a definitive response to the U.S. positions in the indirect negotiations on release of the 52 Americans.

Moreover, the supreme authority in Iran, Ayatollah Ruhollah Khomeini, for the first time was quoted as approving this response, official described as "final answers" that hold the key to immediate release of the hostages.

The big question -- which should be resolved within a day or two through Algerian intermediaries -- is the nature and detail of the "financial guarantees" Iran is demanding as the final step in the negotiating process. According to U.S. officials privy to all the details, this phrase was not previously used by either side in the exchanges of the past six weeks.

If the "financial guarantees" turn out to be U.S confirmation of the previously offered arrangements for freeing Iranian assets, this can be quickly accepted here and the hostages soon released, in Washington's view.

But this is the most optimistic interpretation of the Tehran announcement, and optimism has been rarely justified in the past. The Washington sources, therefore, were apprehensive that the mysterious "guarantees" may turn out to be complicated and difficult, and -- in the worst case -- beyond the legal ability or political authority of the American administration.

Despite occasional reports to the contrary, administration officials said the positions as provided to Iran in the recent indirect discussions represent the maximum that the United States can or will do in the present circumstances. "If they want more, we are in big trouble, because we have gone as far as we can. There is nothing left," said an official.

Another nagging worry in official circles is that, despite the words of Prime Minister Mohammed Ali Rajai, the "financial guarantees" may not be the only Iranian condition for a final settlement. Some past public statements have made Iran's terms sound much simpler than they turned out to be when they reached Washington.

For all these reasons, an atmosphere of suspense and a sense of impending movement pervaded the high reaches of official Washington, but without much confidence that the end of the long, tangled road to release of the hostages is in sight. While there is no doubt that Tehran's statement is a very important development, it is premature to think that it will be an unmixed plus, or even that it will turn out to good news when carefully examined, an official said.

White House press secretary Jody Powell cautioned reporters against "any kind of overly optimistic interpretation of the public statements" in Tehran. Powell said it would be "particularly unfortunate" at the Christmas season to project great optimism at the development, since "we have no idea in God's earth what it means."

A White House official told reporters that late last week the Algerian diplomatic team now in Tehran relayed to Washington "additional information" from Iranian authorities, and that the United States responded through the same channel over the weekend.

State Department officials, however, sought to minimize the significance of this exchange, saying that it was only one of a series of similar exchanges in recent weeks with the Algerians, who are the chosen intermediaries of Iran. They said the most recent exchange, referred to by the White House officials, did not change the U.S. substantive position and did not not cast any light on the response Iran is now preparing to make.

As of late yesterday, Washington officials said there was no word from the Algerians in Tehran that they had received the response announced by Rajai, nor was there a clear timetable for conveying the response to Washington. The expectation here was that the official view would be on its way within a day or two, ending the suspense and bringing the hostage negotiations into a critical new phase.