Argentina and Britain continued in a belligerent standoff today over Argentina's occupation of the Falkland Islands as Buenos Aires, echoing London's stance, said it was prepared to use military force. The government here also announced economic sanctions against Britain and tight security measures on Falklands residents.

Both governments said fighting broke out yesterday between Argentine troops and British Marines as Argentine forces moved on South Georgia Island, a dependency of the Falklands 900 miles to the southeast.

A communique issued by the ruling junta here said that three Argentine soldiers had been killed in the engagement. No British casualties were reported.

British Defense Secretary John Nott said in London that 22 Marines in Grytviken, an Antarctic observation post on South Georgia Island, were overwhelmed after destroying an Argentine helicopter and damaging a corvette patrol boat.

Argentine President Leopoldo Galtieri responded to reports of a British naval mission to the Falkland Islands--called the Malvinas here--early this morning by saying that if Argentina is attacked, the nation "will give battle . . . in arms, with all the means available."

In London, Nott reiterated that Britain will use force "if necessary" to retake the South Atlantic archipelago.

The fighting on South Georgia marked the second instance of armed British resistance to Argentina's invasion of the archipelago, which began early Friday with a well-planned air and naval move against the Falkland island group during which one Argentine officer was killed.

Argentina has claimed the entire network of islands, about 300 miles off its southern coast, ever since its garrison was expelled by the British in 1833. It ordered the Falklands' 1,800 residents to remain in their homes until further notice yesterday and imposed tight restrictions "to consolidate the control gained over the population," the government news agency reported.

In English- and Spanish-language radio broadcasts and in notices delivered in the island's town of Port Stanley--now called Puerto Rivero by the Argentines--residents were told that anyone found outside his or her home would be arrested, according to the report.

Those suffering "serious inconvenience" because of the restriction could attach a white handkerchief to their doors, the bulletin said, and would be helped by military patrol.

Last night, the Argentine government also responded to the freezing of Argentine assets in Britain by imposing a similar freeze on British holdings here. Economics Minister Roberto Alemann also told reporters after a late meeting at the presidential palace that beginning Monday, Argentina will make foreign payments only for imports with bills due within two days.

The second measure was apparently designed to prevent the crisis with Britain from further unhinging Argentina's wobbly economy, which suffers from a shortage of foreign reserves and one of the world's highest annual inflation rates, about 130 percent.

Gen. Mario Benjamin Menendez, the newly appointed Argentine military governor of the Falklands, told reporters before leaving for the territory this morning that "we are initiating now a period of consolidation" during which "military action against an eventual English threat is still important to emphasize."

It was not clear today whether Argentine forces were encountering continued resistance on the islands, where British and Argentine troops fought a three-hour gunbattle in front of the governor's house in Port Stanley Friday morning, according to eyewitness reports published here. Argentine journalists reported yesterday that several British Marines may have escaped into the interior of East Falkland Island during the takeover, but these reports have not been confirmed by either government.

In addition to the order restricting residents to their homes, the military decrees issued yesterday said that Falkland residents can be jailed for 180 days for "actions that disturb community normality" and 60 days for "irreverent conduct toward patriotic symbols."

Jail terms also are specified for drunkenness and inconsiderate gestures toward Argentine military personnel.

The announcement of restrictions came after Argentine journalists toured Port Stanley yesterday and reported that the atmosphere was calm and the predominantly English-speaking population was accepting the new Argentine presence quietly, if with some resentment.

Films broadcast on Argentina's government-controlled television last night showed residents calmly walking along the streets and children playing on swing sets, apparently before the new restrictions were imposed. But residents interviewed on the broadcast complained in clipped English of the Argentine presence.

"We're not happy that our country should be taken over," said Falklands postmaster Bill Everidge to an Argentine interviewer on the television broadcast. "I've lived here for 50 years. I'm British, my family came from England, and I'm very unhappy that my country is not British anymore."

Two British journalists expelled from the islands today by Argentine forces reported that damage to Government House in Port Stanley indicated that the initial fighting to take over the islands had been serious.

Simon Winchester wrote in the Sunday Times that residents of the Falklands were bitter about Britain's failure to defend the islands and fearful of British retaliation.

He reported that residents wept as the British governor, Rex Hunt, left Port Stanley in full ceremonial uniform, with sword and plumed hat. The governor was flown to Montevideo, Uruguay, along with the Marines.

In a series of interviews on government television and with Argentine journalists flown to the islands, officials here have announced plans to transplant gradually Argentine government, education, services and culture into the 4,618 square miles of the disputed territory. They have insisted that Friday's military movement was a "repossession" of territory that has always been Argentina's.

Although the events leading to the crisis began in mid-March with the raising of an Argentine flag on South Georgia by a group of Argentine scrap workers, Argentina's claim to the island has been a major patriotic issue in the country for generations, and reports of a possible invasion were circulating in Buenos Aires as early as mid-January.

Successive Argentine governments have portrayed the rocky, treeless islands as important to Argentina's position as a strategic power in the South Atlantic and have stressed the possibility of rich petroleum reserves in the area. But decades of negotiations with the British government produced virtually no progress in the dispute, and Argentine officials had grown increasingly frustrated with what they considered Britain's intransigence.

Argentine political sources have described the Falklands as a major priority from the beginning of Galtieri's three-month-old government. The new leader has sought to win a popular following for the military government amid a severe economic crisis and growing calls for a return to democracy after six years of military rule.

Long before the invasion, political analysts here were saying that the Galtieri government hoped to resolve favorably either the Falklands issue or another heated border dispute Argentina has with Chile, thus fulfilling, in either case, decades of fervent patriotic hopes among the country's 28 million citizens.

Earlier this year, Galtieri's administration moved in the dispute with Chile over three small islands in the Beagle Channel at the tip of South America, declaring that it would no longer honor a peace treaty it signed with Chile on the issue a decade ago.

But aggressive Argentine action on the dispute with Chile was seen here as more dangerous than a move against the Falklands. Argentina and Chile nearly went to war in 1979 over the issue, and a military move by Argentina in the Beagle Channel would almost certainly lead to a major military confrontation.

In contrast, Argentine officials here apparently hope that Britain, separated by 8,000 miles from its colony, ultimately will back away from taking military action to regain control.

At the same time, the Argentine government has shown no sign of being willing to retreat from its own position, despite a U.N. Security Council resolution yesterday calling on it to withdraw its forces from the archipelago. The Foreign Ministry here has responded to that action by looking for support to Argentina's more sympathetic Latin American neighbors, and it has asked for a meeting of the Organization of American States on the crisis early this week.

The Associated Press reported from New York that Foreign Minister Nicanor Costa Mendez said Sunday that Argentina would respect the Security Council resolution to cease hostilities and negotiate with Britain, but he made no mention of the council's demand that Argentina withdraw its forces from the islands.

The military government appears to have rallied substantial labor and political support for its actions only a week after the largest and most violent antigovernment demonstrations since rule by the armed forces began. The endorsements have only seemed to grow more forceful in the face of international opposition, and newspapers and politicians here continued to call today for the government to retain its control over the island.