British Prime Minister Margaret Thatcher held urgent meetings with senior Cabinet ministers today on new U.S. ideas for solving the Falkland Islands crisis as Britain began talking about the possibility of starting limited warfare in the South Atlantic while continuing to negotiate.

As the fight-and-talk proposal evolved, the Defense Ministry continued to decline comment on the whereabouts of the British naval task force after Argentina charged that two warships had reached the vicinity of remote, sparsely inhabited South Georgia Island 800 miles east of the Falklands.

Foreign Secretary Francis Pym flew back from Washington overnight after two days of talks with U.S. Secretary of State Alexander M. Haig Jr. and went directly to 10 Downing Street to report to Thatcher in a two-hour meeting. Thatcher, Pym and other key advisers--a group that has been dubbed the "War Cabinet"--met for three hours tonight to discuss ideas for a settlement proposed by Haig.

A Cabinet spokesman said Pym had been in contact with Haig tonight but that Britain had "real difficulties" with the American proposals and the government was "still not hopeful" of a peaceful settlement.

Thatcher left tonight for Chequers, the prime minister's country estate, where she will mull over the most important decision of her political career--whether to launch hostilities.

Argentine Foreign Minister Nicanor Costa Mendez, who was scheduled to fly from Buenos Aires to Washington Saturday night, told reporters that there "is still a possibility of an agreement" with Britain, Washington Post correspondent Jackson Diehl reported. Argentine officials reiterated that the government was still insisting that any agreement should provide some assurance that Argentina would eventually obtain sovereignty over the Falklands.

In Washington, the State Department said Costa Mendez was scheduled to meet Haig on Sunday.

Thatcher and Pym have both refused to rule out the use of force at any stage, but there has been an assumption that talking, with Haig as intermediary, would end once fighting began.

By continuing talks even if fighting starts, Britain would seek to avoid responsibility for ending the negotiations--although it remains to be seen whether Argentina would continue to bargain.

The problem for Thatcher is that the credibility of her threat to use force will rapidly diminish if the military does not act soon, now that the task force is reaching the Falklands.

"What has changed," a British source said, "is the position of the task force."

A variety of highly placed sources said that British military action would not necessarily be delayed either by a report to Parliament by Pym on Monday or a meeting the same day in Washington of the Organization of American States where Argentina will seek Latin American support against Britain.

Referring to reports that U.S. officials doubt Britain would use force, the British source said: "The Americans know better than that. They know we mean it when we say we would use force."

There were plenty of war jitters today.

One British popular newspaper reported that South Georgia had been invaded, causing the Defense Ministry to issue a denial, saying the task force "has not landed anywhere." A spokesman said that the Argentine report that elements of the fleet were off South Georgia could be an effort to try to influence the OAS meeting.

British correspondents aboard the aircraft carriers in the task force said pilots of the Harrier vertical-takeoff jets are taking turns sitting strapped in their cockpits on the flight decks waiting to be scrambled. Argentine reconnaissance Boeing 707s have flown over the task force three times and have been challenged by the Harriers, but no shots have been fired.

Reuter reported the Defense Ministry as saying Britain had warned Argentina through Swiss intermediaries that "all Argentine aircraft, including civil aircraft engaged in surveillance of British forces, will be regarded as hostile and are liable to be dealt with accordingly."

In response to that, a Foreign Ministry spokesman in Buenos Aires said his government informed the U.N. Security Council that Argentina will use its "legitimate right of self-defense."

The crews are on defense alert, second only to battle stations alert, meaning that half the men are at their posts at any time.

The task force suffered its first known casualty last night when a transport helicopter went down in the frigid waters of the South Atlantic. The pilot was rescued but the other crewman is missing and presumed dead.

In London, there was a small sign that hostilities may be imminent. The Defense Ministry, which so far has been willing to brief only British journalists, has made arrangements to hold briefings on short notice for the hundreds of foreign correspondents here.

Today's popular press carried scare headlines over stories about British Broadcasting Corp. broadcasts of a government message urging Britons to leave Argentina. "Run for your life," said The Sun.

Reports from Argentina claimed that high winds and waves ruled out an imminent assault on South Georgia. The Defense Ministry here said that the weather in the area of the task force is "bad and variable" but would not comment on the military implications.

If Britain does attack, South Georgia is regarded as the most likely first target by many political and military analysts.

The island, discovered by Captain James Cook in 1775, is beyond the range of the Argentine Air Force and is believed to be lightly defended. An Argentine force overran 22 British Marines to capture the island April 3, one day after the Falklands were taken.

The only civilian inhabitants on the island, which is mainly covered by permafrost and snow, are reportedly 13 British scientists.

South Georgia, which is slightly larger than Rhode Island, was once a major whaling station. The disputed landing of Argentine scrap merchants on the island in mid-March marked the beginning of the current Falklands crisis.

The island could provide a rudimentary base for the British, with landing space for helicopters and the Harriers in the event of prolonged hostilities.

Mainly, however, the recapture of South Georgia would provide a boost for British morale and present an unpalatable political fact for Argentina, a military analyst said.

"It would be a cheap victory," he said. "If Britain wants something more than a political presence"--in other words, if it wants to retake the Falklands--"it will have to pay for it."

It is generally believed that Britain does not have enough troops in position yet to attack East Falkland, where most of the 1,800 British residents and up to 10,000 Argentine troops are located. About 1,000 of the 1,500 Marines in the task force are believed to be aboard the requisitioned cruise ship Canberra, which left Ascension Island, 3,500 miles north of the Falklands, yesterday. The Marines would be the main assault group since the task force is believed to lack sufficient air power for a paratroop attack.

Thatcher said Thursday in Parliament that the British title to South Georgia "is quite different from that of the Falkland Islands, and it is a separate dependency," even though it has been administered through the Falklands "as a matter of convenience."

Britain has major interests in the island in relation to the Antarctic, she said.

J.W. Matthew, a former administrator of the island in the 1950s, said in a letter to The Times of London that South Georgia has considerable strategic importance.

"It only needs one bomb on Suez and another on Panama for it to be demonstrated that whoever has South Georgia can dominate the South Atlantic and western Antarctica. Until now peaceful British administration of South Georgia has made this risk quite obscure," he said.