Secretary of State Alexander M. Haig Jr. suddenly reversed plans to leave here this afternoon and continued talks with high-level Argentine officials in what appeared to be a marathon final effort to break a diplomatic stalemate between Argentina and Britain over the Falkland Islands.

Late this evening as Haig finished a six-hour session at the presidential palace here with the Argentine military leadership, officials said the talks would continue and there was no decision on when Haig would leave or whether he would go to Washington or London. It was unclear when the talks would resume.

In a day marked by an atmosphere of tension and confusion, reports here first indicated that the U.S. effort to peacefully end Argentina's armed occupation of the islands had stalled, then, as the talks were unexpectedly extended, they turned to cautious hope of a breakthrough.

British Prime Minister Margaret Thatcher cut short a country weekend late Saturday and returned to London to meet senior advisers for talks on the crisis, The Associated Press reported.

Spokesmen said Thatcher's return did not signify new developments but was a stocktaking session.

Government sources said the indications late Saturday were that Haig will fly to Washington from Buenos Aires and not fly directly to London as originally expected.

The chief obstacle to a solution in the two-week crisis--and the reported cause for the talks' near breakdown today--was the issue of Argentina's claim of sovereignty over the South Atlantic archipelago and how it would be recognized in any possible formula, officials indicated.

Argentina has been willing to agree to a withdrawal of the troops that invaded the islands April 2 if the approaching British war fleet turns back and has suggested possible arrangements for a temporary administration of the islands while negotiations proceed, sources here had said.

However, Argentina has insisted on leaving its flag on the islands, which it calls the Malvinas, as part of an implicit recognition of its sovereignty in any temporary arrangement. Britain has refused to accept such a concession to Argentina's claim.

Reports here this morning indicated that Haig formally proposed--and the Argentines rejected--a tripartite administration of the islands involving British, U.S. and Argentine officials. That proposal, which officials here refuse to confirm, reportedly was turned down in part because it left the sovereignty issue unaddressed.

Argentine and U.S. officials yesterday expressed high hopes that this weekend's meeting would lead to an accord that would halt the British naval fleet and end the threat of a military confrontation in the South Atlantic.

But after talks at the Foreign Ministry adjourned last night and Argentine Foreign Minister Nicanor Costas Mendez gave Haig a message from the ruling military junta, reports spread that no progress has been made.

While officials on both sides refused to make any statement about the success of the negotiations tonight, the Argentine government released a copy of a letter from President Leopoldo Galtieri to Pope John Paul II that bitterly characterized Britain's position.

Galtieri, responding to an appeal by the pope for a peaceful solution, said that Argentina had been making "extremely great efforts" for a solution "well appreciated" by the United States. But, Galtieri added, Argentina will not "humiliate itself before any pretense of wounded pride particularly when it is backed by the use of force."

The government also announced today that it had arrested two Canadians and an American working for the Canadian Broadcasting Corp. in the southern port city of Comodoro Rivadavia. An Air Force spokesman said Tony Hillman, of Chicago, and Canadians John Axelson and David Wilson were held after filming Air Force planes at the air base outside the city.

The government also said that three British journalists arrested Friday after taking pictures of military maneuvers will have a hearing Monday to determine whether they will be charged with espionage.

This morning Haig went to the presidential palace for what was described as a farewell visit with Costa Mendez, President Leopoldo Galtieri and the two other junta members.

Then, as the luggage of the U.S. delegation was being loaded at the airport, U.S. and Argentine officials suddenly agreed to continue the talks. After lunching with Costa Mendez, Haig and other U.S. officials returned to the palace amid reports that a deadlock had been at least temporarily avoided.

The confusion today marked the fragile nature of this round of talks, which--proceeding without schedule--have appeared to be conducted under pressure of an abrupt U.S. departure.

This negotiating style, markedly different from the elaborate preparation made for Haig's first trip a week ago, enhanced the growing sense of tension here as Argentina refuses to back down on its claim to the islands.

As Haig's delegation traveled back and forth today, Buenos Aires was quiet, with no signs of last week's fervent patriotism.

In place of the 100,000 flag-waving demonstrators outside the palace last week, silent knots of spectators waited outside meeting places today, anxious to learn whether a solution had been reached.

Argentine officials who were quick to deliver fiery speeches a week ago have maintained a tight silence about the meetings this weekend.

The Galtieri government is being pressured by growing dissension by political and labor leaders here, who earlier had provided a united front of support for the government's management of the crisis.

The Peronist political party, which dropped an active antigovernment campaign when the islands were invaded and joined in a campaign of "national unity," distanced itself from the government in a statement yesterday calling for a normalization of political activity