The Carter administration, despite its public posture of patience and hope, privately is increasingly fearful that Iran will not go through with what U.S. officials thought was a deal for the speedy release of the American hostages in Tehran.

After almost a week of apparent rebuffs from Iranian authorities, the administration yesterday continued to take a tight-lipped, turn-the-other-cheek attitude toward rising speculation that it had been duped by Iran or had deluded itself into believing it had an Iranian commitment that did not really exist.

In the face of Iranian assertions that the disposition of the hostages -- held since last Nov. 4 -- will not even be considered before April or May, U.S. officials led by President Carter and Secretary of State Cyrus R. Vance have insisted that "progress is being made" and that they expect the United Nations fact-finding mission now in Iran to secure the freedom of the hostages.

But, when pressed about when that is likely to happen, Carter, Vance and other senior administration officials all have been forced to reply that they do not know.

That is in marked contrast to the situation two weeks ago when the U.N. commission was being hammered together under the mediation of Secretary General Kurt Waldheim. Then, highly placed U.S. sources were signaling privately but unmistakably that the commission was the mutually agreed-upon trigger for release of the hostages, with some sources even saying that it would take roughly two weeks to have the captives freed.

Last Saturday, though these optimistic signals were silenced with chilling suddenness when Ayatollah Ruhollah Khomeini, Iran's most powerful leader, unexpectedly announced that the hostage issue would be decided by Iran's new parliament, which is not expected to begin meeting until April.

Since then, U.S. officials, for all their brave public stance, have admitted privately that they do not know what Khomeini's statement means. Washington, they concede, has been unable to find out whether Khomeini's words should be taken at face value as warning that early release isn't in the cards or whether they represent some sort of ploy in the internal Iranian maneuvering from positioning among Khomeini, President Abol Hassan Bani-Sadr and the hostages' militant captors.

As a result, the U.S. response has been to play for time by letting the U.N. commission go forward with its work and see what happens. As one official describes it: "For the moment, we have no option other than to take it one day at a time."

While there is no question that the administration thought it had some kind of understanding about quick release of the hostages, there now is considerable doubt about how specific the deal was and what went wrong.

Publicly, the administration's only admission that an apparent bargain was struck has been the assertion, restated by Vance on Wednesday, that the U.N. commission's mandate, agreed to by all parties, was "to hear the grievances of the Iranians and also to bring about the speedy release of the hostages and thus end the crisis."

In private, U.S. sources insist that "speedy release" was never intended to mean a time span stretching into April, or even later, as another Iranian leader, Ayatollah Mohammed Behesti, hinted on Wednesday. Prior to Khomeini's statement Saturday, the sources said, the Iranians had never said a word about April and, if they had, the United States would have refused to approve the commission.

Similarly, the sources added, in the negotiations over creation of the commission, the United States felt it had Iranian quid pro quo -- that sending the commission to hear Iranian complaints against deposed shah Mohammad Reza Pahlavi was tied specifically to the hostages' freedom. As a result, the sources said, current Iranian assertions that the issues were not linked are not true.

But, while there seems to be agreement across the board among administration sources on these points, some of the information being given out privately by U.S. officials about other aspects of the deal contains discrepancies.

During the final stages of negotiations on the U.N. commission, for example, some sources said explicitly that its work was expected to take about two weeks and that the hostages' release would coincide with the end of that period.

In the past few days, however, other sources have said that the Iranians, at the last minute, refused to commit themselves to a specific timetable for the release, but did leave both U.S. and U.N. officials with the clear impression that they would act more speedily than now appears to be the case.

There are disagreements, too, about other points, including whether Waldheim, in his go-between role, unintentionally may have misled Washington or Tehran about what the other was proposing or agreeing to.

Still, while U.S. officials concede that some misunderstandings may have occurred, they insist that the general outlines of the agreement, including a rough definition of "speedy" release, were clear to all sides and that the difficulties now being encountered seem to be the result of after-the-fact changes on the Iranian side.

What is not clear, the officials stress, is whether, as one puts it, "We are being had." By that, he means the United States doesn't know if it was subjected to an Iranian attempt to reap the publicity benefits of the U.N. commission without making good on its part of the bargain.

Another possibility, to which U.S. officials presently seem more inclined, is that the hitches represent an attempt by Khomeini, who was side-lined with heart trouble during the negotiations, to assert his authority over Bani-Sadr, a moderate on the hostage issue.

If that is the case, U.S. officials say, Bani-Sadr's apparent attempt to defer to Khomeini could have the hopeful result of allowing the release movement to get back on track with only minimal delays. But, they also add, Washington presently has no clear picture of the state of play within Iran and can only wait until the U.N. commission finishes its work, probably in the next week or two, before it knows whether the crisis is heading toward resolution or new tensions.