U.S. officials and Algerian intermediaries yesterday began a new round of intensive talks marking the latest stage in the long effort to win release of the 52 American hostages in Iran.

The day-long opening meeting was held at the State Department under conditions of strict secrecy that offered no clues to the state of play in the hostage situation except for a statement that the Algerians had been assured by Iranian authorities that the 52 captives, prisoners since Nov. 4, 1979, "are in good health."

Beyond that, department spokesman John Trattner would say only that "the Iranian position as conveyed by the Algerian delegration seeks clarification of certain aspects of the U.S. response" that was sent to Tehran 12 days in answer to the conditions set by Iran for freeing the hostages.

In private, U.S. sources said the talks with the Algerians, who have been designated by Iran's revolutionary leaders as their representatives in dealing with Washington, are likely to take several days. After hearing the Iranian point of view, the sources continued, the Algerians probably will be asked to convey a new U.S. response to Tehran.

That process, the sources added, could turn into a de facto exercise in shuttle diplomacy by the Algerians; and the sources said there was no way of telling at this point when or how it will end. The sources, while noting that the request for clarification appears to be an encouraging sign that Iran isn't slamming the door on further discussion, said: "We're still in the ball game, but we've got a long way to go yet."

Iran's four conditions, set by that country's parliament, call for a U.S. pledge not to interfere in Iran's affairs, the freeing of Iranian assests in this country frozen by President Carter, the dropping of all U.S. claims against Iran and the return of the late shah Mohammad Reza Pahlavi's wealth.

The U.S. response on these last two points -- those involving claims against Iran and the shah's assets -- are understood to have stated that American law poses restraints on how far the president can go in meeting Iran's demands. However, the Iranians are believed to be seeking further American concessions on these points, and it is known that those are the main topics that the Algerians were asked to pursue in their discussions here.

The three Algerian envoys -- Ambassador to the United States Redha Malek, Ambassador to Iran Abdelkarim Ghraieb and Seghir Mostefi, governor of the Algerian central bank -- came here Tuesday after several days of consultations in Tehran. Previously they had been briefed intensively on the U.S. response by Deputy Secretary of State Warren M. Christopher who went to Algiers on Nov. 10. s

After the U.S. proposals were delivered to Tehran, a number of Iranian officials made conflicting statements about the nature of Iran's official reaction. Although U.S. officials are known to have been advised informally about The Iranian reaction, the meeting yesterday was the first chance the U.S. government has had to hear at first hand what the Iranians think about the next steps.

A new confusing note was added to the situation yesterday when the speaker of the Iranian parliament, Hojatoleslam Hashemi Rafanjani, told a press conference in Beirut that Iran would be prepared to release some of the hostages if the United States fulfills some of the conditions.

"We expected America would not be able to meet all the conditionss but every time they move a step forward we will release some of the hostages," Rafsonjani said. He had said previously that Washington appeared willing to meet the first two conditions immediately but that those involving the claims and the shah's wealth would require some time to sort out.

When it promulagted its terms, the parliament said some hostages would be released in phased increments if the United States fulfilled some of the conditions, but Iran so far has made no move toward doing that. In addition, Rafsanjani, in his comments yesterday, gave no sign that Iran intends to ease any of its demands.

"We do not understand the workings of American law, but we expect the Americans to solve the problem which was caused by them," he said. "We, for our part, have set our laws which are simple. It is now up to America."