Carefully worded U.N. and White House statements yesterday launching the United Nations' "commission of inquiry" on Iran have opened a new, and possibly final, chapter in the long-running epic of the American hostages.

The desired end, the release of the captive Americans, is firmly in mind in New York and Washington, and there is cautious confidence in both the intentions and the capability of the key figure in Tehran, President Abol Hassan Bani-Sadr.

Nevertheless, as the confusing events of yesterday demonstrated, beginning with a crisis call to the State Department at 1:30 a.m., there remain several important hurdles and many a potential slip on the road to success. At the moment, officials are still walking on eggs.

While U.S. officals declined to confirm the remark of commission member Mohammed Bedjaoui of Algeria that "we have a gentlemen's agreement for the hostages' release," it is clear that that international panel is considered here to be a major step toward that goal. It would not have been approved otherwise.

It is also clear, however, that several other steps will be necessary beyond the work of the commission. While the timetable is still uncertain, these steps may come after the panel's report is completed and made public in a week or two.

Bani-Sadr has consistently laid down three requirements for U.S. action leading to release of the hostages. There has been much top-level discussion here, and a considerable amount of confidential diplomatic maneuvering, on meeting these conditions.

One of the requirements is that the United States agree never again to interfere in Iran's internal affairs. President Carter went out of his way to address this yesterday, by saying in his statement on the U.N. commission that "the United States has no desire to interfere in the internal affairs of Iran."

The second condition for Bani-Sadr is that the United States accept Iran's right to take action to extradite the former shah and return his wealth. According to official sources, the United States has worked out ways in which this can be done.

The third condition, which the Carter administration is reported to be "still chewing on," is a U.S. recognition of guilt or "self-criticism" about its role in past Iranian events.

This is by far the most difficult for Carter, who has made it known through spokesmen and in talks with members of Congress that the United States will not "admit guilt." This message has been passed to the Iranians.

While final decisions apparently have not been made, it appears likely that, in the end, the United States will make some statements in acknowledgement of its prior role in Iran, but only at the point when it is nearly certain that these statements will bring about the hostages' release.

In undertaking delicate, difficult and in some respects demeaning negotitions over the past several weeks, the administration was acting on the belief that at last, in the person of Bani-Sadr, there was a central Iranian authority with both the will and the way to accomplish the hostages' release.

Bani-Sadr made it clear from the very first that he opposed the taking of the hostages, and as early as Nov. 13, nine days after the event, he proposed to U.N. Secretary General Kurt Waldheim that the United States accept an investigation of "the guilt of the former shah and its consequences" as a step toward resolving the crisis. At that point, Bani-Sadr was acting foreign minister with a tenuous power base. The United States did not accept his plan.

Bani-Sadr's election as president by an over-whelming vote Jan. 25 and his subsequent appointments as chairman of the Revolutionary Council and commander in chief of the armed forces have steadly increased his authority. The post-election steps and Bani-Sadr's uncontradicted claims to have the support of Aytollah Ruhollah Khomeini have been taken here as signs that he has the clout to deliver.

Khomeini's radio broadcast in Tehran last night repeating the demand for the shah's extradition and seeming to praise the "youths" at the U.S. Embassy, was a chink in Bani-Sadr's armor. But the circumstances of the broadcast were not clear, and it was considered important that Khomeini did not link the return of the shah to the release of the hostages.

That link of shah-for-hostages was broken earlier by Bani-Sadr in a move that made the current negotiations and maneuvering possible. The Iranians president demands the extradition of the shah, but not in exchange for the hostages. To obtain the hostages, he demands that the United States recognize Iran's right to extradition.

Because of remaining uncertainty about the Iranian position, the United States insisted that Tehran's invitation to the U.N. commission be presented in writing. This prudent condition delayed the announcement of the commission for several days. For a few hours early yesterday, it threatened to derail the commission entirely.

Bani-Sadr's telegram of invitation to Waldheim, received in the early hours yesterday, referred to the commission as "a court for an inquiry" into past U.S. intervention through the regime of the former shah, and said "their treachery, crimes and corruption" would be investigated.

In some respects, including the reference to "a court," this seemed to go beyond the previously negotiated understanding.

Assistant Secretary of State Harold H. Saunders was awakened with the news of the cable from Tehran at 1:30 a.m. By 4 a.m. the word had reached the president, and at 5:30 a.m. Saunders and Deputy Secretary of State Warren Christopher met with Carter at the White House.

After on-again off-again signals at the United Nations. Waldehim was able to clarify the mission of the fact-finding group by about noon EST.A few minutes later he made the formal announcement.

Administration officials would not confirm a report by James Reston in The New York Times that Carter had resisted approval for the U.N. commission to precede the release of the hostages, but was persuaded to relax his stand by Waldheim and Secretary of State Cyrus R. Vance.

The earlier U.S. position was that while a package deal might be discussed in advance, nothing tangible, such as the work of a U.N. commission, could precede the release of the hostages. About a week ago, American officials at the United Nations began to say privately that "a commitment" relating to the release of the hostages -- rather than their actual release -- must precede its "effective working."

Now even that requirement is in doubt, in the literal sense of the word "commitment," American officials appear to have far more than a mere hope, and considerably less than a certainity, that the commission and the other steps will bring about the release.

Given the U.S. objective of obtaining the safe release of the hostages, there is little alternative to seeking to work with Iran's new president and the United Nations. There are simply no alternatives available, official sources conceded.

With national pride as well as hostages at stake, it will not be easy for two prideful nations to thread their way to a solution in the days ahead. But, for the first time, it seems within the realm of possibility.