The Carter administration welcomed the appointment of a United Nations commission on the Iranian crisis yesterday with a carefully worded statement that stressed the commission will explore American grievances against Iran.

"The United States understands that the commission will hear the grievances of both sides," said the statement issued by the White House shortly after appointment of the commission was announced by U.N. Secretary General Kurt Waldheim.

Officials said, however, that the commission will not hear any formal presentation of American grievances, beyond today's statement that serves as an expression of the U.S. position against Iran.

"The American people are deeply aggrieved that Iran, after guaranteeing the protection of our people, has taken them hostage and held them in intolerable conditions for 108 days," the statement continued. "The United States has no desire to interfere in the internal affairs of Iran, but it does insist on the prompt return of the 53 Americans now illegally held in Tehran."

While the White House statement emphasized the American side of the international dispute, its working appeared to have been worked out during the lengthy negotiations that led to yesterday's announcement by Waldheim and the official blessing of the commission by the U.S. and Iranian governments.

Both the statement and administration officials also stressed yesterday the commission's mandate to see each of the American hostages but not to subject them to "Interrogation" or "cross-examination."

"It is vital, however, for the commission to determine that they are all present, and to assess their condition," the statement said.

Briefing reporters a senior administration official was reluctant to discuss the U.S. understanding with Waldheim and Iranian officials on when and how the hostages are to be released as a result of the appointment of the commission and its forth-coming inquiry into the regime of the deposed shah of Iran.

The White House statement, however, pointedly noted that "an early resolution of the crisis between our two countries . . . requires the release of the hostages."

The administration official stressed Waldheim's description of the commission as a "fact-finding" body, as opposed to a tribunal, that will hear both Iranian and American grievances. He also said it "particularly important" to the United States that the commission ascertain the condition of each hostage.

The complex and delicate nature of the negotiations was underscored yesterday with the announcement of an unexpected three-day delay in the scheduled departure of the commission for Tehran because of "technical reasons relating to preparation and scheduling."

The administration official said Waldheim "was on the phone most of the night last night" working out the final details. He said the State Department officials most deeply involved in the negotiations began work at 1:30 a.m. yesterday.

At 4 a.m., President Carter telephoned the State Department group, and by 5:30 yesterday morning the group was at the White House meeting with Carter, the official said.

"I don't think any reasonable person would want to guarantee that this was the last sleepless night we will see in this process," he said. "This will continue to be a difficult process."

While appointment of the commission was clearly an optimistic sign, the process aimed at freeing the hostages remained clouded with uncertainties. It is known that several steps remain to be agreed upon, and among the questions known still to be troubling administration officials is whether Iranian President Abol Hassan Bani-Sadr has consolidated his power sufficiently to force release of the hostages by Iranian militants.

The administration official also stressed the attempts to form a commission that might lead to release of the hostages have been under way since shortly after the takeover of the American embassy in Tehran in November.

This is a politically important point to the president, who is under fire from Sen. Edward M. Kennedy (D-Mass.) for allegedly refusing to consider appointment of a commission until recently.

The official said the first U.S. overtures to Iran on the possibility of a commission were made in November, but nothing came of them.

"The circumstances are different now than they were in November," he said, and apparent reference to the rise to power of Bani-Sadr.