Deputy Secretary of State Warren Christopher left Algeria yesterday after delivering the U.S. response to Iran's conditions for freeing its 52 American hostages, but there was no sign that an end to the captives' plight is in sight.

The State Department issued a terse statement late in the day announcing that Christopher was returning home after two days of explaining the U.S. response to Algerian Foreign Minister Mohammed Benyahia and other Algerian officials. It added that Algeria, designated by Iran as its intermediary, had agreed to arrange "prompt transmittal" of the proposals to Tehran.

U.S. officials said privately that they had no information to indicate that the secret response, or an outline of its contents, had been communicated to Iran as of last night. They added, however, that fuller details about where the situation stands would not be available until Christopher's arrival home about noon today. His Air Force jet developed engine problems and Christopher's team was forced to spend last night in Shannon, Ireland.

At the same time, Tehran radio yesterday reported that the Carter administration has told Iran that President-elect Ronald Reagan will accept the administration's decisions concerning the possible release of the hostages, according to Agence France-Presse. It quoted the broadcast as saying the U.S. message was delivered by Swiss Ambassador Erik Lang to the speaker of Iran's parliament, Hojatoleslam Ali Akbar Hashemi Rafsanjani.

In Tehran, the governor of Iran's central bank, Ali Reza Nobari, told the Reuter news agency that he had heard of the American reply's contents through "channels" and added, "They are cool toward us." Nobari said that, based on what he had heard about the American response, he could not be optimistic about an early resolution of the hostage crisis.

The Iranian conditions, adopted formally by that country's parliament on Nov. 2, call for the United States to pledge not to interfere in Iran's affairs, for the freeing of Iranian assets frozen in this country, for the dropping of all U.S. claims against Iran and for the return of the late shah Mohammad Reza Pahlavi's wealth.

The United States already has said it will not interfere in Iranian affairs, and President Carter has pledged publicity to free the assets once the hostages are released. However, the other two points -- those relating to the claims against Iran and the shah's wealth -- involve legal questions that may be beyond the president's power to resolve.

In an obvious reference to those problems, U.S. sources have described the administration's response as meeting "the spirit if not the letter" of the Iranian demands. When Christopher and a team of expert advisers left for Algiers early Monday, their mission was described as having as its primary goal a careful explanation to the Algerians of each point in the response and how it fits into U.S. law.

That was underscored anew by yesterday's State Department announcement. It said: "During the meeting, Christopher and the U.S. delegation described the background of the U.S. response and explained the financial and legal procedures which would be involved."

According to the Reuter report from Tehran, Nobari said it was his understanding that the United States is sticking to its contention that the president cannot halt private claimants from going into federal courts to pursue their claims against Iran.

He said the Iranian central bank, which has had legal advice from American attorneys, had advised on the wording of the terms to ensure that they could be met under U.S. law.

Nobari noted that Iran has its own claims against American firms that he said had failed to fulfill contracts, and he suggested establishment of a commission to deal with the conflicting claims questions. Such a commission, Nobari said, would be comprised of representatives from Iran, the United States and a neutral third party and would have available funds from an escrow account to settle outstanding claims.

He stressed that the idea represented his personal rather than official Iranian government opinion. But, he noted, the United States has in the past settled similar claims problems with the Soviet Union and China without a resort to court actions that could require years.

Nobari also rejected the idea that the United States has no power to help Iran recover the late shah's assets. He said the United States should issue a declaration of Iran's right to nationalize the shah's wealth, identify those of the shah's assets that are in this country and put them under control of a U.S. government agency until the matter is resolved.

In Algiers, Algerian officials said they did not expect a quick resolution of the hostage problem, but they otherwise refused any comment on the next steps. The general expectation there, though, was that the Algerian ambassador to Iran, Abdel Karim Gheraieb, who was in Algiers for the talks with Christopher, probably will deliber the response to Tehran, perhaps as early as today.

U.S. officials cautioned against reading any significance into Christopher's decision to return to Washington rather than wait in Algiers for the Iranian reaction. They said it was possible that Christopher will return to Algeria at a later time, but stressed that nothing was certain about the next steps in the long diplomatic tug of war over the hostages.