The United States reacted with arm's-length caution yesterday to hints that Iran's revolutionary leaders may be softening the demands they say are the price for the release of the 60 to 65 American hostages at the U.S. Embassy in Tehran.

Carter administraion officials said, publicly and privately, that the newest signals from Tehran are too murkey for the United States to tell whether they are an Iranian trial balloon aimed at finding a basis for negotition or merely a "rhetorical exercise in press-release diplomacy."

The administraion's wary response to the new Iranian move in the test of wills between the two countries highlighted a day of frenetic and confusing developments that included:

The House, reflecting mounting national outrage and frustration over the situation, voted 379 to 0 for a continuing foreign aid resolution containing an express prohibition against any aid going to Iran, even though there was no money for Iran contained in the bill.

President Carter canceled a scheduled town-meeting trip to Philadelphia and an appearance at a Democratic Party dinner in Harrisburg, Pa., in order to remain in close touch with the situation. It was the second trip canceled by Carter since the takeover of the embassy Nov. 4. The other was to have been to Canada last weekend.

Oil prices in the spot market jumped in response to Carter's Monday order halting Iranian oil imports, with some sellers asking $45 to 50 a barrel for crude, although it was not clear whether anyone was buying at those levels.

On the New York spot market, home heating oil prices rose 2 to 3 cents a gallon, but most experts expected only minor dislocations because of large stocks of heating oil on hand.

The State Department revealed that it has established telephone contact with Iranian students holding the hostages in the embassy compound. But department officials stressed that the telephone link was being used essentially for passing family messages to the captives, not for negotiations with their captors.

The International Longshoremen's & Warehousemen's Union announced in San Francisco that no cargo to or from Iran will be handled by union members and no Iranian ships will be served until the hostages are released.

Administratiopn sources said that one option under review for possible use by the president may involve ordering a halt to the training of Iranian military officers and freezing the $775 million Iran has advanced to the United States for purchase of militaty equipment.

The main topic known to be under study in administration circles yesterday concerned statements by two members of the Islamic Revolutionary Council proposing that the United States return deposed Shah Mohammad Reza Pahlivi's fortune to Iran and suport an international investigation into shah's "crimes."

On the surface, these proposals appeared to be a backing away from earlier demands that the shah, who is undergoing treatment in New York for cancer, be returned home forcibly for trial as a criminal. The United States has rejected that demand flatly.

[U.S. officials said last night that the shah requires additional surgery for a neck tumor "the size of a baseball" and that his condition is "getting worse and worse," the Associated Press reported.]

In private some administration sources said these proposals, advanced by acting foreign miistry chief Abol Hassan Bani -- Sadr in a message to U.N. Secretary General Kurt Waldheim and by radio and TV boss Sadegh Ghotbzadeh at a news conference, might be a sign of a genuine Iranian effort to lower the tone of tension between the two countries.

But State Department spokesman Hodding Carter, noting that the proposals had not been spelled out in any detail and had not even been communicated directly to the U.S. government, said: "I'm incapable of dealing with something we don't have before us. We don't have enough to respond in any way useful."

He also underscored the administration's wariness at becoming involved in issues or negotiations that might have the effect of shifting attention from what the United States regards as the central issue: the tug of war over the hostages. He said:

"One point is central. The first question is the release of the hostages. They are being held in violation of international law and bilateral treaties. That is our main focus."

Elaborating privately on the spokesman's public statement, onee administration source said, "They're holding our people in their back pocket, and we can't afford to get sidetracked into discussions that will change the basis of discussion. Also, we've got to see a lot more before we know precisely what the Iranians have in mind and whether there's any hope in pursuing this avenue."

He and other sources said the United States is actively seeking clarification of what the Iranians mean, and added that L. Bruce Laingen, charged d'affaires of the U.S. embassy, who has been in refuge in the Iranian foreign ministry, might be able to obtain some of this clarification today.

Defense Department sources said no decisions have been made yet about whether to try and pressure Iran by halting military training or freezing Iranian cash deposits here. But, they added, training of 273 Iranians, mostly student pilots, at 12 U.S. bases in this country almost certainly will have to be stopped in response to congressional pressure, if for no other reason.

The Iranians are being trained to fly American-supplied planes sold to the shah before his downfall. As a result of related arms agreements with the shah, Iran has deposited in the United States $470 million to cover termination costs for canceling any of the $3 billion arms-sales agreements still alive, through refunds to U.S. defense contractors.

Iran has given the United States another $305 million for spare parts and military equipment to go with weapons it had ordered earlier. In addition, Iran has another vulnerable asset: a warehouse it built at McGuire Air Force Base in New Jersey for temporary storage of U.S.-purchased equipment before it is shipped to Iran.

The administration last week forbade Iran to continue shipping equipment from McGuire. Pentagon officials said yesterday, though, that they did not know the value of the material in the warehouse.

Defense also announced yesterday that the aircraft carrier Midway has been dispatched from Mombasa, Kenya, to the Arabian Sea to join two other U.S. vessels in naval exercises with Britain. But the announcement emphasized that the exercises had been "planned before the takeover of the embassy" and were unrelated to the Iranian situation.

At the White House, presidential press secretary Jody Powell said the public response to the president's decision to halt Iranian oil imports was overwhelmingly favorable.

Powell said 89 percent of the calls to the White House Monday and yesterday supported the president's action and his general handling of the situation. Before last weekend, he said, a much higher percentage of the calls from the public "were much more oriented toward the need to take some action, any action."

State Department officials said that, in the wake of Monday's actions indefinitely halting Iranian oil sales to the United States, there is no evidence that Iran has reduced its production. But, they added, it seems doubtful that Iran will be able to sell at high spot market prices all of the 700,000 barrels a day previously shipped to the United States.

So far, the officials said, Japan appears to be the country most aggressive in trying to pick up the spare Iranian production.

Senior administration officials said that Friday they expect experts further consultations with the 20-member International Energy Agency, made up of major industrial nations. The meeting's purpose, the officials said, will be to discuss further joint conservation measures and the response of consumer countries to an anticipated hefty December price increase.

Officials continue to say in private that an increase of $5 a barrel, which would boost domestic fuel costs by 12 cents a gollon, "is not unlikely."