The State Department, sharply disputing an Iranian statement that the 52 American hostages "are living in beautiful hotels," said yesterday it has reason to believe that many of the captives actually are in prison and that some have health problems for which they are "not getting adequate medical attention."

"We remain deeply concerned about the hostages' situation," department spokesman John Trattner said "Contrary to Iranian reports that the hostages are now housed in luxury hotels, we have reports that a number of them may, in fact be in prison."

The Iranian government, Trattner continued, "has given us on accounting of who is even responsible for the hostages. They haven't respected even the minimal standards of treatment or accountability for the hostages that the international community expects."

According to other sources, from 10 to 15 of the hostages have not been heard from since July, and six have not been heard from since the failed U.S. rescue mission in April.

Trattner's comments were in response to a reported statement Sunday by Iranian Executive Affairs Minister Behzad Nabavi, who was quoted as saying: "They [the hostages] are well treated and content.They are living in beautiful hotels with all sorts of facilities at their service."

The British news agency Reuter quoted "a reliable source" in Tehran as saying the hostages actually are being held in one of the late shah Mohammad Reza Pahlavi's palaces at Nowshahr, on Iran's caspian Sea coast about 75 miles north of Tehran.

Trattner's sharp response was the second example in two days of newly toughened Carter administration rhetoric on the hostage question. A more combative U.S. tone began to become evident Sunday when Secretary of State Edmund S. Muskie, while saying the administration will continue to seek a diplomatic solution to the hostage impasse, termed Iran's latest demands "unreasonable" and beyond the administration's negotiating guidelines.

In the 13-month tug of war over the hostages, U.S. officials have alternated between tough and soft talk, depending on the circumstances. Prior to the weekend, when the United States was awaiting word about Iran's latest terms and when statements by Iranian leaders hinted that an agreement might be near, the tone of official U.S. statements was clearly conciliatory.

For example, when State Department officials were asked about the hostages' condition, they invariably replied by noting that the Algerian envoys, who have been acting as intermediaries with Tehran, were told by Iranian officials last month that the captives were all alive and well.

Department sources said yesterday the more detailed and alarming description given by Trattner does, to some extent, reflect an attempt to influence world opinion and reinforce the U.S. argument that a negotiated solution is necessary both for humanitarian reasons and for Iran's hopes of escaping the isolation into which it has been placed by the hostage crisis.

In addition, the sources said, Trattner's remarks on the incarceration and health of the hostages stemmed, in part, from information contained in letters recently sent by some of the hostages to their families. In a sudden burst earlier this month, approximately 30 of the families received mail from their captive relatives.

However, because of the lack of detailed information on some of the hostages' whereabouts, one source said, "the mosaic that we have put together about the possible location and health of the hostages is very sketchy."

Although Trattner refused to reveal details of what was said in the recent letters, some hostage families confirmed that many were distinctly negative in tone. At least one hostage wrote that he was sick and not getting adequate treatment, and another said that he was cold all the time.

One, Richard H. Morefield, sounded lonely in the letter sent to his wife, Dorothea, according to family members. "Time passes slowly as I have little to do other than to read," he wrote. Morefield added that, upon seeing a family picture sent by his wife, he had mistaken his youngest son, Steven 14, for his 16-year-old brother, Kenneth.

As Christmas approaches, many hostage families said they are concerntrating on the things the captives expect them to be doing at this time of year: shopping, caroling, going to church and holding family dinners.

"Our plans are the same as every year, just exaclty the same," said Gloran Lewis of Homer, Ill., mother of a hostage, Marine Sgt. Paul E. Lewis. "Just us together. We've got three other kids, and two of them had birthdays in the last two weeks. . . . We figure the best thing is to just keep right on going."

Earlier this month, 45 of the 52 families gathered here to be briefed on the negotiations by Undersecretary of State Warren M. Christopher. But, as one frustrated wife said, "It was virtually the same briefing as the one before." She cited a cartoon that depicted the situation as a yo-yo reeling up and down its string with the caption: "Yes, there is definitely movement."

As to the next U.S. move, Trattner said analysis of the Iranian terms, which include a demand that the United States deposit $24 billion with the Algerian central bank before the hostages are freed, was complete and "we are thinking over our next step." In the meantime, he added, the United States was continuing its efforts to arrange some kind of Christmas services for the hostages in Tehran, but stressed he had no new information about whether that will be possible.

One unofficial but outspoken comment on the situation came from Trattner's predecessor, Hodding Carter, who before his resignation from the State Department last summer had been the administration's principal public voice on the hostage situation. Interviewed on the ABC television program, "Good Morning America," Carter said of the Iranian demands:

"It is frankly is kick in the face. It's not something that any government, this one or the next one, can in any way be made to accept. As far as negotiating what they are proposing, that is simply not in the cards."