President Carter has asked the principal allies of the United States to break diplomatic relations with Iran next month if additional political and economic measures have not won the release of the American hostages in Tehran by then.

This deadline, which became known yesterday, would be preceded by growing pressure on Iran by the United States and its allies in an effort to avert a complete break between Iran and the western powers over the hostage crisis.

In an interview yesterday with television correspondents from Britain, France, West Germany and Italy, Carter referred indirectly to a request he made to the allies to sever their ties with Iran if the hostages are not freed in the next few weeks.

Asserting that it would not be appropriate for him to set a deadline for a resolution of the crisis, Carter told the European reporters:

"But we have sent to the heads of nations -- all of those represented by you -- a specific date at which time we would expect this common effort to be successful."

The "common effort" involves additional economic sanctions and political measures that the United States has asked its allies to impose as soon as possible, in the first stage of this newest administration effort to end the crisis that began Nov. 4.

If those measures fail, the efforts would reach a second stage marked by the U.S. allies' breaking diplomatic relations with Iran, according to the plan proposed by Carter within the last few days.

The exact date set in Carter's request could not be learned but was said to be in the first part of May.

The United States apparently has received no firm commitments from its allies for a break with Iran by the deadline. However, administration officials continued to express satisfaction yesterday with what they called "the direction" of the allies' response thus far.

U.S. allies in Western Europe and Japan are much more dependent than the United States on Iranian oil exports and have extensive trade relations with Iran. These countries are known to view the possibility of a break with extreme reluctance and there is no assurance that they would go along with Carter's request.

Administration officials until yesterday had said the United States was asking allies to reduce their diplomatic missions to Iran, not to sever relations. By calling for a diplomatic break in May, the president has substantially increased the demands he is making on the allies as well as the risks involved to the Western alliance should he fail to gain their support.

In the same interview yesterday, the president for the first time spoke openly of using military force to end the crisis were the other measures to fail.

Asked what the United States would do if the Iranian militants harmed hostages, Carter said, "Our action would be very strong and forceful and might very well involve military means.

"If our hostages are injured or if any of them are killed, then we would not delay in taking much stronger action of an incisive nature," he added.

Heretofore, Carter has referred to military measures only indirectly, such as by assertions that the United States will use "every legal power" at its disposal to win the safe release of the 53 hostages.

The interview is to be broadcast on European television stations tonight but portions of it became public yesterday.

During the questioning, Carter's impatience and the extent of the domestic pressure on him to end the crisis were evident.

"We don't have much time," he said. "The American people are ready and eager to see this matter resolved. Under international law, we are a seriously aggrieved party and we have a breadth of options available to us -- economic, diplomatic, military options, as well.

"To the extent that the allies can join with us in making effective the additional diplomatic and economic pressures that might cause the Iranians to release the hostages, then we can forgo the requirement that we take additional, stronger actions," he continued. "We prefer to keep our actions nonbelligerent in nature, but we reserve the right to take whatever action is necessary to secure the safe release of our hostages."

Asked how long he is willing to wait for economic and diplomatic steps to have effect on the crisis, the president replied: "It's not a matter of many weeks or certainly not a matter of months."

On Friday, White House press secretary Jody Powell said the next U.S. moves against Iran will be political and economic, and not involve military measures. A break in diplomatic relations by the allies -- which Carter is asking to occur in May -- presumably would be the final non-military type of pressure available to the United States in seeking to end the crisis.

Carter broke U.S. relations with Iran last Monday, ordering all Iranian diplomats and their staffs out of the United States.

On Thursday, the president stepped up pressure on the allies, saying he was disappointed by the unwillingness of some to join the United States in seeking the hostages' release.