Ignoring a personal plea from President Reagan and risking military retaliation by Britain, Argentina today invaded and took military control of the Falkland Islands off its southeast coast, which Britain had ruled for the past 150 years.

An invasion force of about 2,000 Argentine marines and more than a dozen warships early today seized Port Stanley, capital of the islands, which the Argentines call the Malvinas and have claimed since 1833. Argentina's military government later announced that a lieutenant commander was killed and two other marines were injured, but that no casualties were suffered by the small British defense force of 80 Royal Marines or by the island's 1,900 inhabitants of British descent.

After a day of considerable confusion here about events more than 8,000 miles away in the South Atlantic, Britain tonight broke off diplomatic relations with Argentina, announced military preparations of its own and asked the U.N. Security Council to demand the immediate withdrawal of all Argentine forces from the disputed islands.

Argentina, backed by the Soviet Union and Third World nations, had the Security Council vote postponed at least until Saturday, special correspondent Michael J. Berlin reported from New York.

According to broadcasts and messages from the islands and news agency reports from Buenos Aires, Argentina deployed a large naval force off Port Stanley, and a large number of marines stormed ashore shortly after midnight, surrounding the British governor's house and blowing up the main radio transmitter.

Argentina's move came at a time of mounting domestic unrest for the military government in Buenos Aires and exposed it to the possibility of a confrontation with the British Navy. A small British force, including a hunter-killer nuclear submarine, was reported to be already on the way to the region as a larger force was being marshaled by the British Navy.

In addition to the considerable national pride at stake for both countries, there also are believed to be oil deposits upward of 2 billion barrels under the waters off the Falklands.

The invasion was launched shortly after President Reagan appealed to Argentine President Leopoldo Galtieri in a 50-minute telephone conversation "not to go forward." Today, State Department spokesmen in Washington said, the administration told the Argentine government, "We deplore the use of force to resolve this dispute." It said the United States would press for an Argentine withdrawal in direct contacts and through the United Nations.

Galtieri said in a national radio and television address today that Argentina had "recovered" what it calls the Malvinas, "which by legitimate right are part of the national patrimony." He said the use of force was necessary because Britain had perpetuated its rule over the islands "through an interminable succession of delays and evasions" during diplomatic negotiations during the past 15 years.

But British Prime Minister Margaret Thatcher called the invasion "an act of unprovoked aggression" against what has been a British possession since 1833 and whose residents, most of them sheep farmers, have always insisted on remaining British. The invasion followed a British demand that Argentina remove from South Georgia, an outlying island dependency of the Falklands, a group of Argentine salvage workers who landed there two weeks ago to dismantle a disused whaling station without observing immigration formalities.

While the invasion was being celebrated in Buenos Aires as a patriotic triumph for the military government, it has created a serious political crisis here for Thatcher's Conservative Party government. Amid mounting criticism of its initially low-key response to Argentine invasion threats, Thatcher's Cabinet held three emergency meetings today and scheduled a Saturday session of Parliament for the first time since the Suez crisis debate in 1956.

Parliament was told today that the Thatcher government was "taking appropriate military and diplomatic measures to sustain our rights under international law." The foreign secretary, Lord Carrington, told reporters tonight that Britain was seeking to force an Argentine withdrawal through diplomatic means, particularly the United Nations, but he noted that the U.N. Charter gives members "the inherent right to take action in self-defense . . . to expel or repel an invader by force."

Defense Secretary John Nott told reporters a "substantial task force" of warships, reportedly including two aircraft carriers and several dozen other vessels, was being prepared here for possible use in the Falklands, which are about two weeks' sailing time away. In addition, Nott said, "We have had a substantial number of Royal Navy ships at sea for some considerable period of time." He would not disclose their locations, but informed sources said the nearest to the Falklands was a nuclear-powered, hunter-killer submarine still several days away.

British marines and paratroopers were put on alert at bases here.

At a crowded press conference here tonight, Carrington and Nott were vague on details in answering frequently hostile and skeptical questions about British military preparations and intentions. They denied rumors they might resign and contended that Britain had not been embarrassed by the invasion because the Falklands' great distance from Britain made them difficult to defend.

"I would not want you to draw the conclusion from the fact that the Falklands are 8,000 miles away, that we cannot defend them," Nott added.

Former Labor Party foreign secretary David Owen, now a prominent member of Britain's new centrist Social Democratic Party, said the government had made "a tragic error" by not deploying warships around the islands off the tip of South America at the end of February, when it first appeared the Argentine government was moving toward another in a series of confrontations with Britain over the Falklands since the early 1970s.

"Even if we mount a major show of naval force now," he said, "I think it's going to be extremely difficult to get them back. I want to warn people against believing that Britain can reinvade and get them back."

Like Carrington, Owen emphasized the potential intermediary role of the Reagan administration. While Britain is the closest U.S. ally, the Reagan administration has been seeking closer ties with the Argentine military government and its support for Reagan's strategy in war-torn Central America.

"I have been in touch with Secretary of State Alexander Haig on a number of occasions last night and today," Carrington told reporters. Citing Reagan's telephone plea to Galtieri last night and what he called a "roundly condemnatory" U.S. statement on the invasion today, Carrington said, "the U. S. government has been extremely helpful."

Reagan told reporters in the White House rose garden, "I did talk to the president of Argentina and tried to persuade him not to go forward."

Carrington said Argentina rejected British efforts to negotiate a peaceful solution to the dispute and cut off diplomatic contact yesterday, when the British government became convinced Argentine forces would invade the Falklands. Argentina also ignored a U.N. Security Council appeal last night to avoid force.

According to accounts of the Argentine government and media, radio and telex messages reaching Britain from the Falklands, and British military analysts, the invasion began shortly after midnight.

Argentina had massed an aircraft carrier, heavy cruiser, four destroyers, three guided-missile corvettes, three troop-carrying ships and three submarines off the disputed islands. Military fighter and transport planes and helicopters flew overhead.

Argentine marines stormed ashore at Port Stanley and the nearby airport, bringing armored vehicles with them. The broadcast station, barracks of the British Marine contingent, and the British governor's house were quickly surrounded. The main radio transmitter was blown up and house-to-house searches were begun for small radio sets, according to amateur radio operators broadcasting to Britain.

It remained unclear how much resistance was encountered or whether the 80 Royal Marines, armed only with sidearms, rifles and possibly mortars, were all captured, as Argentina claimed.

A communique issued in Buenos Aires said all British military personnel and civilian officials would be taken to another South American country. The Uruguayan Interior Minister, Gen. Yamandu Trinidad, said the captured British governor and Marines were taken to Montevideo, across the River Plate from Argentina, to be turned over to the British ambassador. He said their stay would be brief.

Official communications with Britain were impaired after the invasion began. Carrington said confirmation of the capture of Port Stanley was pieced together from official Argentine government announcements and fragmentary radio and telex transmissions, some monitored by a Royal Navy ice patrol ship still sailing safely somewhere around the island group.

In the last telex exchange with the Foreign Office here earlier today, an operator in Port Stanley tapped out: "We have lots of new friends."

Asked if the Argentines were in control, the operator responded: "Yes. You can't argue with thousands of troops plus enormous Navy support when you are only 1,800 strong."

After a request to "stand by, please," the telex line went dead.

The Argentine government later announced that the British governor, Rex Hunt, had surrendered and would be flown to Buenos Aires. He was replaced with an Argentine military governor, Gen. Mario Menendez, according to Buenos Aires. A curfew was imposed and islanders were warned not to interfere with the occupying forces, according to an amateur radio operator in the Falklands.

For hours after announcements from Buenos Aires that the Falklands were under Argentine control, British officials told Parliament and reporters they had no confirmation of the invasion. This appeared to prompt increasing criticism over whether the government had responded with sufficient speed as the crisis built in recent weeks.

Despite continuing diplomatic moves by Thatcher's government and the time it will take for British military forces to reach the Falklands, officials, politicians and news media speculated about the possibility of a military clash.

Asked today in Buenos Aires if the Argentine government was ready for war with Britain, whose total military forces are far greater, Defense Minister Amadeo Frugoli told reporters, according to Reuter, "Argentina will continue to defend without hesitation what it considers to be its own."

Special correspondent Michael J. Berlin reported from the United Nations:

Britain called on the Security Council to adopt without delay a resolution demanding the immediate withdrawal of all Argentine forces from the Falkland Islands.

Most diplomats expressed doubts that Britain could muster the necessary nine-vote majority for its draft. The resolution also demands an immediate cessation of hostilities and calls on both sides to "seek a diplomatic solution to their differences" over the archipelago.

At a council session this morning, British Ambassador Sir Anthony Parsons reported the "massive invasion," which he called a "blatant violation of international law."

Argentina's ambassador, Eduardo A. Roca, replied that the islands had been restored to his country's sovereignty, thus ending "a situation of tension and injustice," which had been a constant threat to peace.

Roca rejected the British charge of aggression and said Britain's interests in the islands were negotiable, but sovereignty was not.