The United States was involved in intense but apparently unsuccessful diplomatic activity last night amid new military and political developments in the Falkland Islands conflict.

Secretary of State Alexander M. Haig Jr., according to a State Department spokesman, conferred by telephone with Peruvian President Fernando Belaunde Terry about 7 p.m. following the Peruvian's announcement in Lima of a peace initiative to stop the fighting.

Shortly before midnight Washington time, the Argentine junta announced it had rejected a plan that it attributed to Haig "through the intervention" of Peru's president for a settlement of the dispute.

The new proposals "essentially persist in propositions similar to the last proposal of the United States," which Argentina had refused to accept, an Argentine statement said.

The State Department said Haig also had discussed peace proposals with British Foreign Secretary Francis Pym, who left Washington for New York late yesterday after a four-hour meeting with the secretary of state and a 50-minute session with Defense Secretary Caspar W. Weinberger.

Although "a number of ideas were exchanged" in the wake of the Peruvian initiative, the State Department said, "There has been no agreement on anything."

Spokesman Joseph Reap Jr. confirmed that the United States received a diplomatic note from Argentina as that nation reacted to the latest developments in the deepening clash. Reap declined to discuss the contents of the message, which was reported in Buenos Aires to blame the United States for "accelerating the confrontation with Great Britain."

The protest note, according to reports in the Argentine capital, declared that the U.S. shift to support Britain "will leave deep marks in Argentine-American relations."

Neither State Department nor Defense Department spokesmen would comment on the British submarine attack on Argentina's only cruiser near the Falklands.

President Reagan, meanwhile, called a meeting of the National Security Council for today for a briefing on the Falklands crisis, the White House said.

Pym, meeting reporters following his meeting with Haig yesterday afternoon, denied that Argentina had inflicted any damage on the British armada and said, "You can count on the truth and validity of any communiques we may give you from our Ministry of Defense."

It was Pym's first visit here since the talks almost two weeks ago that led to formulation of a U.S. peace plan. Its subsequent rejection by Argentina caused President Reagan to suspend U.S. mediation efforts and declare support for Britain.

"The last time I came to see Mr. Haig in his role as mediator," Pym said as he expressed gratitude for the American position. "Today I have come back to consult with him as an ally."

The British minister said that, while his government wants U.S. logistical help, he had not come with any shopping list and had not made any specific requests of Washington.

A British diplomatic source here said the Peruvian proposal to settle the dispute has been discussed. The source, who asked not to be identified, said the Peruvians first advanced a plan for a 72-hour break in the conflict two or three weeks ago, and that the current proposal may be a refinement of that plan.

It is likely, he added, that Haig discussed the Peruvian ideas with Pym at their lengthy meeting yesterday and that Pym will discuss it in New York with U.N. Secretary General Javier Perz de Cuellar, who is a Peruvian.

Peru's President Belaunde was quoted by wire services as telling a news conference in Lima that Argentina and Britain have agreed "in principle" to a cessation of fighting, but this was not backed up by reports from other capitals.

U.S. officials, speaking before the latest British Defense Ministry report, said privately that the intelligence available to them supported London's claim that the only losses so far were suffered by the Argentines, although they added that fragments from an exploding missile had caused slight surface damage to a British frigate and injured a seaman aboard the vessel.

The officials would not reveal the source of their intelligence. But Rep. Michael D. Barnes (D-Md.), chairman of the House inter-American affairs subcommittee, said he had received similar information. Barnes, who had a detailed State Department briefing yesterday, spoke on "Face the Nation" (CBS, WDVM).

In answering questions about possible U.S. aid, Pym said his talks yesterday were intended to ascertain the specific areas where Washington could provide help. "As our needs become more apparent, then specific requests will be made," he said.

Weinberger said the British minister did not specifically ask for military aid. When asked if the United States was prepared to refuel British planes in mid-air, Weinberger said no U.S. aircraft would be used for refueling a blockade. But he added that America would continue allowing the British to refuel on Ascension Island.

Earlier, Sen. Charles H. Percy (R-Ill.), chairman of the Foreign Relations Committee, said on "Meet the Press" (NBC, WRC) that U.S. help would be limited primarily to supplying fuel and communications assistance.

Barnes was asked if the United States will provide C5 Galaxy transport planes to ferry supplies to Ascension Island, which is being used as a resupply point for the British forces. He replied:

"I think that the United States would be prepared to do that, although we have not yet been asked . . . But we expect the British to request some assistance shortly."

Administration officials, speaking privately, agreed that U.S. assistance initially would involve mainly fuel and communications gear, as well as the likely use of American transports to move them quickly to Ascension Island.

If the conflict should become protracted, these officials added, the British probably also would require additional supplies of food and possibly ammunition, and they indicated that Washington is inclined to provide that kind of help as well.

Pym also said he hoped that the U.S. peacemaking effort, which plunged Haig into almost three weeks of intercontinental shuttle diplomacy, might be revived at some point. But, in a view that privately was backed up by U.S. officials, he said there seemed no hope of that as long as Argentina maintains its intransigent demand that its sovereignty over the Falklands be acknowledged.

"Sorry, that cannot be allowed," he said. "They must not remain with their claim of usurping sovereignty. Also they've got to withdraw their forces from the islands."

He expressed hope that the economic pressures being brought to bear against Argentina, coupled with Britain's recapture of South Georgia island last week and Argentina's apparent inability to penetrate the British exclusionary zone, "will concentrate their minds" on the desirability of becoming more flexible.

"I reckon that there are a lot of very worried people running around Buenos Aires at this moment," Pym said.

Reagan, who returned here yesterday from Knoxville, Tenn., was asked on his arrival about the possibility of the Soviets' coming to Argentina's aid. He replied: "That could get pretty messy. Let's just hope they don't."