The Carter administration said yesterday it will continue to permit the children of deposed shah Mohammad Reza Pahlavi, who died Sunday, to attend school in the United States and to be visited here periodically by their mother, the former empress.

State Departmet spokesman John Trattner said the U.S. government will stand by the commitments it made regarding the shah's family prior to his departure from the United States for Panama last December.

At the time, White House chief of staff Hamilton Jordan and White House counsel Lloyd Cutler met with the shah at Lackland Air Force Base hospital in Texas and agreed to specific understandings about what help the United States would provide in exchange for his agreement to leave the country.

The main points of the still-secret agreement covered the conditions under which the shah could return to this country for medical treatment. But they also are known to have included a promise that his four school-age children could continue their education here and that their mother, now living in Egypt, could visit them regularly to supervise their care and schooling.

Trattner said that, while the family's plans are unclear, he understood that at least some of the children "probably will return here to school in the fall" and added that the shah's widow "still has the right to visit them."

He dismissed as a "hypothetical question" a suggestion that the widow might now seek permission for permanent residence here. The administration, he added, would consider what to do about such a request if and when it is made.

Trattner, speaking publicly, and other U.S. officials, in private, continued to insist that there is no way of currently assessing the effects of the shah's death on the fate of the 52 American hostages in Iran.

Although the hostages' militant captors had said the return of the shah was necessary for the release of the captives, U.S. officials, including Secretary of State Edmund S. Muskie, have said repeatedly in recent weeks that the principal obstacle to resolving the hostage crisis was the absence of a strong central government in Iran.

Several officials said privately yesterday that still appears to be the case, and they added that the outcome of the hostage situation will depend primarily on the slowly evolving process of political development within Iran.

Asked about militant Iranian demands that the United States return the shah's wealth to his country, Trattner repeated the longstanding U.S. position that this is a legal question and that any claims against the shah's assets in this country should be pursued through the courts.

The spokesman also said he knew of no plans to try and meet the militants' demands by freeing the more than $8 billion in Iranian government assets that were ordered frozen by President Carter following the taking of the hostages last Nov. 4.