Deputy Secretary of State Warren Christopher flew to Algeria yesterday with the formal U.S. response to Iran's conditions for freeing the 52 American hostages whose captivity has made the worsened U.S.-Iranian relations a center of international crisis for more than a year.

Christopher, accompanied by a team of senior U.S. officials, arrived in Algeria one week after Iran's parliament announced its conditions for releasing the hostages.

Christopher handed the U.S. reply, the contents of which are a closely held secret, to Algerian Foreign Minister Mohammed Benyahia. The Algerian government, which Iran has designated its representative in dealing with Washington, is expected to relay the American response to Tehran within hours.

[In Tehran, meanwhile, former foreign minister Sadegh Ghotbzadeh was reported released from prison after the intervention of Ayatollah Ruhollah Khomeini in what was seen as a favorable sign for swift release of the hostages. Ghotbzadeh was imprisoned Friday after a dispute with hard-liners from the Islamic Republican Party, whose struggle with Iranian moderates is considered a potential obstacle to winning the hostages' freedom.]

Informed sources have described the response as very detailed and specific proposals intended to meet the spirit if not the letter of Iran's demands, but U.S. officials said they had no immediate way of knowing whether the response will succeed in resolving the deadlock that has been the almost all-consuming preoccupation of American foreign policy for the past year.

The Iranian conditions call for a U.S. pledge not to interfere in Iran's affairs, the freeing of Iranian assets frozen in this country, the canceling of all U.S. claims against Iran and the return of the late shah Mohammad Reza Pahlavi's wealth.

These last two demands -- relating to the claims and the shah's wealth -- involve legal questions that could be beyond the power of President Carter to meet. For that reason, the U.S. reply on these points is understood to fall short of strict compliance with the Iranian demands, but the administration is hopeful that Iran will accept them as a good-faith gesture of the maximum effort the president is able to make.

In an apparent underscoring of that point, State Department spokesman John Trattner put great emphasis yesterday on the "high-level nature" of Christopher's mission and described its goal as making clear to Iran, through the offices of Algeria, the seriousness and sincerity with which the American proposals have been formulated.

Accompanying Christopher were several of the senior officials who have grappled with the hostage situation extensively over the past year and who are most expert in the technicalities of the Iranian demands. They are Deputy Treasury Secretary Robert Carswell, Harold H. Saunders, assistant secretary of state for Mideast affairs, Roberts Owen, the department's legal adviser, and Arnold L. Raphel, a special assistant to Secretary of State Edmund S. Muskie.

Trattner also said that the details of the U.S. response have been communicated to representatives of president-elect Ronald Reagan, who has made clear his understanding that Carter retains the responsibility for dealing with the hostage situation as long as he is in office.

Although the internal situation in Iran has shown signs of a possible new power struggle between revolutionary hard-liners and moderates, U.S. officials said last night that they had no indications of a loosening of the consensus among most Iranian leaders that the time has come to try and dispose of the hostage problem.

For that reason, some of the best informed officials, while conceding that they do not really know what will happen, expressed belief that there is a good chance of the U.S. proposals being accepted.

Informed sources here said the United States asked the Algerians last Thursday if they would receive Christopher. The sources added that the State Department received an affirmative reply Saturday afternoon, and Christopher then made plans to leave Sunday night. His actual departure was at 1 a.m. Monday.

According to the sources, Carter gave his formal go-ahead for the mission on Sunday. Although the president was at Camp David, the sources said he had been kept informed throughout the various stages of drafting the response and did not require any extensive briefing or consultation on the result.

Trattner characterized the mission as an "open-ended visit," but added: "I don't expect it to be days and days or weeks and weeks." In private, the sources said that if there was a likelihood of an Iranian reply going to Algiers, Christopher probably would wait to receive it. But, they stressed, it was unclear whether developments would move in that direction.

Trattner also said the United States does not expect Algiers to become a negotiating forum for a meeting of Chirstopher with Iranian officials. "You can rely on that," he said.