Prime Minister Margaret Thatcher, celebrating "the fine victory of our armed forces" on the Falkland Islands, told Parliament today that she had moved immediately to restore British administration there.

She said that British troops had taken 15,000 Argentine prisoners of war after the Argentine commander on the islands surrendered last night--a far larger Argentine force than had been previously reported on the islands. She warned Argentina that Britain would hold up the release of some high-ranking prisoners until Argentina agreed to a blanket declaration that all hostilities in the 10-week war had ended between the two countries.

In Argentina, Leopoldo Galtieri, the chief of the military junta, warned that the conflict over the Falklands would continue if Britain restored its administration on the islands, correspondent Jackson Diehl reported.

"I hope we have restored once again the dominance of Britain, and let every nation know that where there is British sovereign territory, it will be well and truly defended and will never again be the victim of aggression," Thatcher told Parliament. The packed but subdued House of Commons reflected a prevailing mood of relief in Britain today after the euphoria last night that greeted the first news of negotiations for an Argentine surrender.

British officials and military analysts have said that at least 3,000 Scots and Welsh guards and Gurkhas--a third of the British troops now on the Falklands--will remain on the islands as a permanent garrison.

Phantom jet fighter-bombers would be added to Harrier jump jets and Rapier antiaircraft missile systems for air defense, according to these sources, and a few warships and nuclear-powered, hunter-killer submarines would protect the islands from the Argentine Navy.

Thatcher said the former colonial governor of the Falklands, Rex Hunt, and exiled members of the executive and legislative councils of the islands' 1,800 inhabitants "will return as soon as possible." Hunt and the commander of the victorious British ground forces on the Falklands, Royal Marine Maj. Gen. Jeremy Moore, "will in effect act as civil and military commissioners," Thatcher said, to "bring life on the islands back to normal as quickly as possible despite the difficult conditions and the onset of antarctic winter."

Britain sent a message to Argentina through the Swiss government today "seeking confirmation that Argentina, like Britain, considers all hostilities between us in the South Atlantic--and not only on the islands themselves--to be at an end," Thatcher said. "It is important that this should be established with clarity and without delay.

"Until we have achieved a cease-fire with the mainland as a whole," she said, British forces will continue to hold a number of Argentine prisoners, "particularly officers and commanders of the forces." A Thatcher aide explained that the government was concerned that Argentina might mount new air strikes against British ships or troops despite the surrender of all Argentine forces on the islands.

The prisoners apparently include the Argentine commander on the islands, Brig. Gen. Mario Benjamin Menendez, who agreed to surrender the Argentine garrison. Thatcher said that approximately 15,000 prisoners of war were taken as a result of the surrender and that the prisoners would be returned to Argentina as soon as possible.

Thatcher described "immense practical problems" of caring for "substantially more" Argentine prisoners than expected. "The weather conditions are severe," she said, "permanent accommodation is very limited."

The number of Argentine forces on the islands previously had been reported at about 7,000 troops in the capital of Stanley in addition to smaller garrisons on West Falkland.

"Proposals have been made to the Argentine government for repatriation of all the prisoners in the context of a general cessation of hostilities, but we have not yet had a response," the aide said.

"The truth is, we have a major humanitarian relief problem on our hands," said the Thatcher aide. Officials said more food and water, as well as shelter and transportation, were needed for the Argentine prisoners, many of whom were reported to be suffering from hunger and exposure.

Thatcher said she believed the United States would be able to help with Hercules military transport planes. She told Parliament that U.S. assistance during the conflict "has been splendid" and that Britain had received "everything we asked for" in logistical and material aid, although she refused to disclose specifics.

In Washington, the Reagan administration has agreed in principle to assist in the transportation of Argentine prisoners of war once arrangements for their return have been made, according to British Embassy officials. Such assistance as well as possible U.S. emergency relief in the Falklands, was taken up with Secretary of State Alexander M. Haig Jr. yesterday by British Ambassador Nicholas Henderson.

On another development, two influential U.S. senators expressed concern that British military efforts to garrison and protect the Falklands would weaken the British contribution to the Atlantic alliance, thus requiring greater efforts from the United States.

Those expressing concern, Democratic Leader Robert C. Byrd (W.Va.) and Republican Whip Ted Stevens (Alaska), quoted Haig as telling a leadership meeting at the White House that such British efforts would have an impact on the Atlantic alliance.

Thatcher repeated that she hoped other countries, including the United States, also would help guarantee the future security of the Falklands, but she vowed once again that "if necessary we shall do this alone."

"We shall uphold our commitment to the security of the islands," she said. "Our purpose is that the Falkland islands should never again be a victim of unprovoked aggression."

The cost of this has been estimated at between $200 million and $500 million a year on top of the $2 billion already believed to have been spent retaking the Falklands from the Argentine forces who seized them on April 2. More money will be spent, Thatcher said, on physical rehabilitation and economic redevelopment of the islands after the brief but intense military occupation and fighting.

"Mines must be removed, the water supply in Stanley is not working," Thatcher told Parliament. "There will be other urgent tasks of repair and reconstruction.""After all that has been suffered," she said, "it is too early to look much beyond the beginning of the return to normal life. In due course, the islanders will be able to consider and express their views about the future."

A 1976 report recommending sweeping economic and social changes on the Falklands to redistribute land ownership, increase income from sheep farming, and exploit offshore fishing and oil resources will be updated quickly and acted upon, Thatcher said.

Lord Shackleton, the author of the report, which was largely ignored for years, has said the large British garrison remaining on the Falklands will have a major impact on the islands' economy and way of life.

"When the time is right," Thatcher said today, "we can discuss with the Falkland islanders ways of giving their elected representatives an expanded role in the government of the islands."

She again indicated she expected this eventually to take the form of local self-government under British military protection within the commonwealth of former British colonies.

She ruled out making the islands a United Nations trusteeship, as the opposition Labor Party here has advocated. Thatcher said she fears this could open them up to Argentine settlement and an eventual share in sovereignty.

British troops "did not risk their lives to have a U.N. trusteeship," Thatcher told Labor leader Michael Foot in Parliament. "They risked their lives to defend British sovereign territory, the British way of life and the right of British people to determine their way of life."

Thatcher also ruled out future negotiations with Argentina over sovereignty. "We do not need to negotiate with Argentina or the United Nations or anyone else about British sovereignty of the Falkland Islands," she said. "I do not intend to negotiate in any way except with the people who live there, she said."

Britain today asked its European Community partners to continue economic sanctions against Argentina until the military government in Buenos Aires declares that all hostilities have ceased.

The current community president, Belgian Foreign Minister Leo Tindemans, said its members were considering what to do. A meeting of community foreign ministers might be called, he said in Brussels today, "if action in favor of peace develops."

Thatcher, who had celebrated the first news of British victory late last night with champagne in her House of Commons room with senior government ministers, today postponed until next week a trip to New York to address the United Nations special session on disarmament.

Queen Elizabeth II, whose second son, Prince Andrew, is a combat helicopter pilot on the British task force flagship, the aircraft carrier Hermes, was described by her spokesman today as "delighted and relieved" by the Argentine surrender. "She is very pleased and proud of the courage, determination and professionalism of the servicemen and all those involved down there," said Buckingham Palace press secretary Michael Shea.

Emblazoned across the front pages of Britain's popular tabloid newspapers this morning were large headlines proclaiming, "Victory" and "We've won." Television and radio news broadcasts were extended, and long special programs on the Falklands were rushed onto the air.

Steadily increasing public support for the Falklands war had boosted Thatcher's Conservative Party to unprecedented leads over the opposition parties in public opinion polls. The party has won two convincing victories in recent elections to fill vacant seats in Parliament.

Although Thatcher's popularity could climb even higher immediately after the British military victory, political analysts expect much of this support to erode as post mortems of the crisis are conducted and other issues, including the battered British economy, return to the front pages.

Thatcher pledged in Parliament today to set up soon an independent commission to investigate whether the war could have been avoided.

The British Foreign Office has been blamed by political critics and press commentators for failing to react swiftly enough to Argentine signals and warnings that the Falklands might be seized after what the Argentines considered 17 years of fruitless British-Argentine negotiations. Thatcher's widely respected foreign secretary, Lord Carrington, resigned along with two aides just days after the Argentine invasion April 2.

Defense Secretary John Nott also came under attack for reductions in Britain's surface Navy, including the announced intention to scrap the only Royal Navy ship in the South Atlantic, which critics said encouraged the Argentine junta to misjudge the British commitment to defend the islands.

Nott acknowledged that lessons have to be learned from the Falklands war. Military analysts here forecast that defense spending may be significantly increased and the Royal Navy allocated a larger share of resources after a reassessment of British military needs.