The United States has set a traget date of mid-May for a major reassessment of the long-running Iran crisis, with the clear implication that much stronger steps may be ordered than in the absence of progress toward release of the American hostages.

According to administration officials, leaders of several allied nations were informed by President Carter in telephone conversations late last week of the target date for the U.S. reassessment. Word of the timetable has also been passed to the authorities in Tehran, the sources said.

State Department spokesman Hodding Carter, in a reference to the self-imposed deadline, said yesterday the United States intends at "a time certain" to reassess the Iranian situation "to lay the basis for decisions on what is necessary in the way of further actions." The spokesman did not publicly identify this "time certain," but it is mid-May, according to official sources.

This target date for a U.S. reassessment has a complex and confusing history in administration policymaking and the confidential dialogue with U.S. allies.

Originally selected three weeks ago under different circumstances for a reason that no longer holds forth, the mid-May date now has taken on a life of its own as a potential turning point in the hostage saga.

According to accounts from official sources, here is what happened:

On March 22, Carter and his senior foreign policy advisers conducted a day-long review at Camp David, concentrating on the discouraging state of the Iran negotiations. Efforts to free the hostages through the U.N. commission and channels to Iranian President Abol Hassan Bani-Sadr had reached a dead end. Carter decided a new tack was necessary.

Bani-Sadr was to be given a deadline of March 31 for the promised transfer of the hostages from control by their militant captors to control by the Iranian government. If this were not done, the United States would take new economic and political steps against Iran on March 31, and the threat of military action would be revived.

U.S. allies in Europe and Japan, along with a few others, were informed of these developments by a confidential message dispatched March 25 over the signature of the president. This message called on the allies to join in exerting pressure on Iran in order to stave off the necessity for the United States to take more forceful and dangerous actions later.

The allies were also informed, the sources said, that the United States might call on them to break diplomatic relations with Iran by "the middle of May" if other nonmilitary measures failed to produce results by then. Mid-May was chosen because it would give the other economic and political steps time to work, and because it would give Iran time to sort out its political authority.

In late March, the second round of elections for the new Iranian parliament was expected in April. The parliament was expected to convene and possibly address the future of the hostages by early May.

In this context, the mid-May timetable was a logical target date for stronger steps. But after it was established, several developments occurred:

Due to widespread charges of fraud in the initial voting, the second round of parliamentary elections was postponed until early May. Because of this, Iran's parliament is not expected to meet until June. This timing is important, because all the often-conflicting power centers in Iran are agreed that the parliament will debate and decide the hostages' future.

Bani-Sadr, under prodding from Washington and its allies, tried openly to bring about transfer of the hostages and was stymied. This latest rise and collaspe of hopes led to bitter disappointment in the United States and renewed political pressure on Carter to take stronger action on behalf of the hostages.

Carter announced a new series of measures on April 7, including the break in Washington's diplomatic relations with Iran.Originally this step had been expected later in the spring. And now the administration has redoubled its appeals to U.S. allies to take strong new measures of their own.

The president surprised and upset the allies last weekend by revealing publicly that there is a "specific date" for allied action in the hostage crisis. And yesterday the mid-May date surfaced in new form -- as a date for U.S. assessment of the need for forceful future steps.

U.S. officials concede that it is unlikely that the Iranian parliament will meet, or be on the verge of meeting, by the mid-May target date for Washington's reassessment. Hence there is only a marginal chance for a major new Iranian decision on the hostages' status by that time.

At home, the establishment of a mid-May timetable for reassessment is likely to intensify the expectation of, and pressures for, decisions at that time on last-resort U.S. actions such as military steps.

The pressure, in fact, could mount sharply even sooner, especially if Carter suffers reverses in Tuesday's Pennsylvania primary and other political tests.

In the meantime, some interim steps that may be taken at home or abroad could bear on Carter's standing with the Pennsyvalnia voters. The administration is reportedly considering an additional nonmilitary action of a complicated nature against Iran in the next few days.

And high U.S. officials have asked European governments to decide on their next economic steps against Iran by the April 21-22 Common Market foreign ministers meeting in Luxembourg.