Administration sources said yesterday that Iran's latest terms for freeing the 52 American hostages appear to contain conditions difficult for President Carter to meet -- a verdict that effectively dashed hopes of the captives being released by Christmas or soon afterward.

But, the sources added, it is not clear whether the Iranian message, received here yesterday, represents Tehran's final word on how far it is willing to go toward reaching a compromise or whether there is enough flexibility in its position to warrant another American try at breaking the impasse.

The sources, who declined to be identified, described the message as an intricately detailed document of 10 to 15 single-spaced, typewritten pages, and said it would take several days, at least through the weekend and probably longer, to analyze it fully.

When that analysis is completed, the sources continued, Carter will have to decide whether there appear to be enough points of potential agreement between Washington and Tehran to seek another round of indirect negotiations or whether the gap is so wide that the best course would be to turn the issue over to the incoming Reagan administration.

The most likely result, the sources said, is that the Carter administration will seek through Algeria, the go-between in the indirect contacts, to present new counterproposals to Iran. But, the sources stressed, as of last night the administration deliberately was leaving open the option of not responding further to Tehran and referring the matter to President-elect Ronald Reagan on the theory that he will be able to deal with it from a position of greater authority than a lame-duck president can.

This gloomy assessment was in marked contrast to the hopes that had been raised here in recent days by statements from various Iranian leaders implying that the revolutionary government was anxious to resolve the hostage situation quickly and was narrowing its differences with the United States over the terms of release. Despite cautionary warnings from Secretary of State Edmund S. Muskie and other top administration officials, these statements fanned a wave of rumors that the hostages, held since Nov. 4, 1979, might be on their way home in time for Christmas.

But, the sources said yesterday, the message given Algerian envoys after 15 days of talks in Tehran has left U.S. officials with the impression -- at least after a first reading -- that the Iranians still are insisting on an almost literal, letter-by-letter compliance with the four conditions set by the Iranian parliament, the Majlis, on Nov. 2.

These conditions were that the United States promise not to interfere in Iran's affairs, that Carter release Iranian government assets frozen in this country after the hostages were taken, that the United States drop all claims, including those by private companies and individuals, against Iran, and that the wealth of the late shah, Mohammad Reza Pahlavi, be returned to Iran.

According to the sources, the latest Iranian message addresses each of these points in detail, including a spelling out of the steps Iran wants taken for their implementation. Although the sources were reluctant to discuss details, they said the main problems, as has been the case since the beginning of negotiations, center on the claims against Iran and the deposed shah's wealth, and an apparent Iranian unwillingness to accept that the U.S. legal system imposes restraints on how far any American president can go to satisfy these demands.

A report yesterday by the official Iranian news agency, Pars, quoted Behzad Nabavi, an aide to Prime Minister Mohammed Ali Rajai, as saying that the United States must deposit Iran's "gold and confiscated wealth" with the Algerian central bank before the hostages can be released. U.S. sources, while confirming that was correct, said it was only one fragment of a much longer, complex set of Iranian proposals for regaining control of their assets.

The sources said such a transfer of at least part of the assets to Algeria was "not beyond the realm of possibility" once other matters had been settled. But, they added, before that question can be addressed, a mechanism for settling U.S. claims against Iran must be agreed on, and they stressed that not such agreement has been reached.

In addition, the sources continued, the two sides have not agreed on the total value of the frozen assets. Iran claims that its money, gold and other property, such as military equipment, tied up in the United States are worth $14 billion. U.S. officials, who initially estimated the frozen assets at approximately $8 billion, since have conceded that the amount is higher, but they have refused to reveal their latest estimate.

In regard to the shah's wealth, Pars quoted Nabavi as saying that the United States must give "acceptable guarantees as goodwill for a proper implementation" of its return to Iran. The U.S. sources said that the Iranian message appeared to be ambiguous about the meaning of that demand, and that it required further study.

The United States is known to have told Iran it will assist in identifying the shah's assets in this country and might even offer advice on how best to seek recovery through the U. S. courts. But, the sources said, the Iranians have been advised emphatically that the president has neither the legal power nor the inclination to simply seize the property belonging to the shah's heirs or to send it out of this country without an appropriate court judgment and order.

The sources stressed that this position cannot be changed. They added that if the Iranians continue to insist on measures barred by U.S. law, there can be no agreement on the condition involving the shah's wealth.

Publicly, U.S. officials refused to say anything except that they were studying the Iranian message and that a further round of negotiations may be in the offing. Perhaps the best signal that the administration has abandoned hope of resolving the hostage issue soon came when State Department spokesman John Trattner said an effort is being made to see if Christmas services can be arranged in Tehran for the captives.

Asked whether that meant there was no expectation that the hostages are close to the end of their ordeal, Trattner replied: "Yes, that is the implication."