Efforts to free the American hostages in Iran moved another step forward yesterday when U.S. diplomats received the official version of the Iranian government's conditions for their release and began considering how to respond to the demands in ways that will end the year-long deadlock over the captives.

Echoing the positive tone set by President Carter in his nationwide television address Sunday night, Secretary of State Edmund S. Muskie unexpectedly appeared before reporters to say that developments in the hostage issue "should be viewed as initial steps in a process which will require time, patience and diplomacy."

"There has been progress.However, much remains to be done," Muskie added. Other U.S. officials said privately that the administration must now begin a probing process aimed at exploring and clarifying what actions the United States can take that will satisfy the Iranian conditions and bring the hostages home.

That, the officials emphasized, is a process likely to take days rather than hours; and they went out of their way to discourage speculation that any or all of the 52 hostages might be released before American voters finish going to the polls in today's presidential election.

U.S. officials announced yesterday that the text of Carter's Sunday statement had been forwarded to the Tehran government. Although the announcement spoke only of the Carter text, reliable sources said the message contained additional information, but they refused to disclose the contents.

The major new development in the diplomatic cat-and-mouse game over the captives came yesterday afternoon when Algerian Ambassador Redha Malek made a 10-minute call on Harold H. Saunders, assistant secretary of state for Mideast affairs, to deliver the official English and Farsi versions of the four conditions set Sunday by the Iranian parliament, the Majlis. Algeria had represented Iran's interests here since Carter broke diplomatic relations last April.

The English text of the communication, which was being kept secret, was being studied by U.S. officials last night to see how it compared with the Farsi version and with the unofficial English translations of the Iranian conditions as they were read publicly in the Majlis on Sunday.

Administration officials who have examined the English text said last night it is not very different from the unofficial translation, but that there are enough differences to merit exploration.

State Department sources said the U.S. reply wll be dispatched to Iran after completion of the study of the text. The sources said the U.S. response may be sent as early as today, though this timing is still uncertain.

In broad outline, the Iranian demands called for a U.S. pledge not to interfere in Iran's affairs, the freeing of Iranian assets in this country frozen by Carter, the canceling of all U.S. public and private claims against Iran, and the return to Iran of the late Shah Mohammad Reza Pahlavi's wealth.

The last two conditions -- those involving claims and the shah's wealth -- pose some potentially difficult legal problems that could be beyond the power of the U.S. executive branch to meet. For that reason, the administration is especially anxious to determine whether the Iranian demands on these points are meant literally or whether Tehran will be satisfied by more limited U.S. steps that can be presented as expressions of American goodwill acceptable as a symbolic meeting of the Iranian conditions.

Reliable sources said they doubted that the answer would be found merely through examiniation of the documents received yesterday and that further probing, though either direct or indirect negotiation, undoubtedly will be necessary to get the required clarification.

However, the sources, while saying that developments look promising, stressed that no actual negotiations are under way yet; the main question that appeared to be preoccupying the administration last night was how to open a channel that will permit the necessary exchanges between Washington and Tehran.

The announcement from Tehran that Algeria has agreed to take over "the issue" of the hostages, plus further developments during the day, indicates that the North African country is likely to be the main channel for indirect discussins with Iran, administration sources said last night. Before he delivered the documents from Tehran, Malek met yesterday morning with Deputy Secretary of State Warren Christopher at U.S. request to begin exploration of the role Algeria will play.

Muskie, in his unexpected appearance to read a statement at the State Department's daily press briefing, welcomed "reports that the Algerian government will be involved" as one of the positive developments that have given the administration cause for hope.

In that connection, he and other officials also called special attention to the announcement from Tehran yesterday that the Iranian government intends to take control over the hostages from the militants who have been their captors since Nov. 4.

But, while U.S. sources saw that as an important further sign that the major power centers within Iran have coalesced behind the idea that the hostage impasse should be ended, they also warned that all manner of unexpected developments could loom up to cause unforeseen complications.

In that regard, U.S. officials were understood to be especially nervous about today's scheduled march by Iranian students and militants to the American Embassy compound in Tehran.

The sources said there were "some suggestions" that the hostages, who reportedly have been brought together in the compound, will be removed before the march takes place. But they recalled that twice in the past militant demonstrations at the embassy were instrumental in scuttling deals to free the hostages, and, they said, it therefore is difficult to assess what effects the march today might have on the situation.

State Department spokesman John Trattner, in announcing that Carter's Sunday message had been sent to Tehran via the Swiss Embassy there, refused to confirm reports that the communication contained additional information.

However, Swiss Embassy spokesmen said the message given Iranian President Abol Hassan Bani-Sadr expressed Carter's satisfaction that the Majlis had come to a decision and his willingness to seek ways of ending the deadlock. The spokesmen stressed that Carter's message was intended as an acknowledgement of the Majlis action and not as a reply to the Iranian conditions.

Trattner, who spoke before the Iranian documents were received here, insisted that the United States was not using any diplomatic channels to try to pursue the matter and would not until the official Iranian version was in U.S. hands and had been studied for clues on how to proceed further.

Reliable sources said, though, that some of the channels used by the United States in the past to communicate with Iran have been working in recent days to get a better understanding of Iranian intentions. The sources added, however, that these preliminary probes have not advanced very far or produced much in the way of information.

One sign that the administration expects the matter to drag on for at least several more days was the unofficial revelation that Muskie is canceling a four-nation visit to Latin America that he had been scheduled to begin Thursday. State Department sources said formal announcement of the visit's postponement will be made as soon as all four governments have been notified formally.

Despite its potential significance for today's elections, both Carter and his Republican challenger, Ronald Reagan, appeared to be trying to keep low profiles on the hostage issue as they pursued their campaigns yesterday.

"Don't know yet," was Carter's response when questioners asked if he was encouraged about the hostages. Reagan, in a speech recorded for broadcast last night, said, "There is nothing I want more than their safe return . . . . When they have returned, all of us will be turning to the concerns that will determine the course of America in the next four years."