Britain and Argentina offered pessimistic assessments yesterday of the prospects of a diplomatic settlement of their increasingly tense confrontation over the Falkland Islands, while U.N. peace talks headed toward what officials there described as "a final stage."

British Prime Minister Margaret Thatcher said in a radio interview last night, "We've gone as far as we can go" in making concessions to avoid more fighting over the islands, which Argentina seized April 2. She indicated that she retained a slim hope that the U.N. negotiations would succeed. "We've been at this for six weeks, and we're having one last go to see if we can get a peaceful settlement," she said.

In Buenos Aires, Argentine government sources said the only hope for averting another round of fighting would be new concessions by Britain. "The ball is with Britain," one official said. "I don't see any way we can get the U.N. talks moving if Britain doesn't move a bit."

Britain's European Community partners, overcoming objections from Italy and Ireland, agreed last night to extend month-old economic sanctions on trade with Argentina for one more week.

The only fighting in the South Atlantic reported yesterday was the predawn shelling by a British warship of Argentine military positions around Stanley, the Falklands capital, according to correspondents with Britain's naval task force. The almost daily shelling of Argentine occupation forces has been described in London as "softening up" the defenders for a British invasion.

Britain's U.N. ambassador, Sir Anthony Parsons, who broke off the talks late last week to travel to London for new instructions, returned to the United Nations yesterday. Parsons presented the instructions to U.N. Secretary General Javier Perez de Cuellar but refused to reveal them. Parsons said only that Britain was "still engaged in very serious, earnest and determined efforts to achieve a negotiated settlement."

Diplomats at the United Nations privately expressed pessimism, saying that time pressures and the large gaps remaining between the two sides made any settlement unlikely. Even Perez de Cuellar, before meeting with both sides last night, appeared to eschew his usual optimistic tone, telling reporters only, "We are at the final stage of our exercise."

Beginning with a speech to Conservative Party workers in Scotland during the weekend and continuing with last night's radio interview, Thatcher appeared to be preparing the public for an invasion and the increased British casualties military analysts say are bound to result.

She told interviewers, "There's no division of opinion" about an invasion among her "war cabinet" of senior ministers and defense chiefs.

"We argue about things; of course, we do," said Thatcher. "There's so much at stake. You discuss every aspect; of course, you do. You owe that to the lives of the people who are going to be risked. And you owe it to their families. You owe it to all our people."

Asked if she feared losing the support of world opinion, the prime minister said, "If we succeed, and I believe we shall, we shall have the quiet acclaim and approval of all who believe in democracy. They will think, 'Thank goodness someone's stood up for international law, someone's stood up for their own people, someone's stood up and been loyal to those who are loyal to them.' "

Thatcher said Argentine President Leopoldo Galtieri could still avoid large-scale casualties in a battle with "an act of statesmanship" by deciding to withdraw his forces and making major concessions in the negotiations. If he doesn't, Thatcher said, "We make him go."

Thatcher said she would go no further in compromising the principle of self-determination for the 1,800 islanders.

She also indicated that Britain would take a harder line on the Falklands' future status if it has to repossess them by force. Government sources said public opinion would make it more difficult to negotiate away sovereignty after a bloody battle to recapture the islands.

Thatcher's strategy again received public support in a new opinion poll taken for the British Broadcasting Corp. Of those polled, 53 percent said British forces should invade the Falklands within a week, while 27 percent favored more negotiations and 11 percent opposed invasion at any time. Also, 62 percent said the Falkland residents should have the final say on their future and 55 percent opposed any eventual transfer of sovereignty to Argentina.

The British Defense Ministry acknowledged yesterday that two British helicopters had crash-landed in snow on South Georgia Island three days before Britain recaptured it from Argentina April 25. The ministry said none of the commandos aboard the helicopters, sent in as a pre-invasion force, was injured.

The pessimistic evaluation from Buenos Aires of the U.N. talks came as the Argentine military command reported that one supply boat had been set afire and another damaged in British air attacks around the Falklands Sunday.

Military communiques said that the 4,600-ton cargo ship Rio Carcarana had been set afire by British warplanes in the channel between East and West Falkland and that the Bahia Buen Suceso, a 3,100-ton vessel, had been damaged.

The official reports said that there were no casualties on either ship.

A communique issued late yesterday charged that several civilian installations in Fox Bay, which lies south of Darwin in East Falkland, had been destroyed by British Sea Harrier attacks. A bomb also fell near a house inhabited by civilians in Darwin, but it failed to explode, the communique said.

Argentine officials cited the continued British attacks on the Falklands as proof that London has yet to concentrate seriously on a diplomatic solution to the confrontation.

In contrast, they said, Argentina has made concessions in the U.N. talks, softening the conditions it has demanded for future negotiations over the territories.

Argentina is still insisting that conditions be attached to the agreement that would direct the talks toward an inevitable recognition of Argentine sovereignty over the Falklands, government officials said.

Although an aide to Argentine envoy Enrique Ros returned to New York for the reopening of the U.N. talks yesterday, government officials said he carried no significant changes in the Argentine position. "We have been flexible enough," one official said.

With Buenos Aires newspapers reflecting the official pessimism, the capital seemed somber yesterday under a cold rain as the country waited for a widely expected British ground assault on Argentine troops dug into the Falklands.

Leading newspapers have carried analyses in recent days speculating on the expected British attack. One report by the news service Noticias Argentinas, quoting military sources, predicted a heavy bombardment of positions around Stanley to divert attention from a mass landing elsewhere on the islands.

These officially sourced reports have concluded unanimously that no British assault could withstand the counterattacks of Argentine air forces based on the mainland and artillery implanted on the Falklands.