As British troops landed in the Falkland Islands yesterday, the White House reiterated its pledge to "meet our commitments to Great Britain" but stressed that "there will be no involvement whatsoever of U.S. military personnel in the conflict in the South Atlantic."

At the same time, a high administration official said the sharply escalating fighting has pushed the battle between Britain and Argentina into a dangerous and unpredictable new phase in which one side probably will have to gain a decisive military edge before there is likely to be a chance to get the fighting stopped.

The official said that, given the intensity of the battle now, the military edge could tip within days.

As he described it, the British might be able to defeat Argentine forces on the islands rather quickly. If that happens, however, it is possible that the British forces could be vulnerable to prolonged and repeated air strikes from the Argentine mainland from an air force four times the size of the roughly 40 British jets in its navy task force. The result could be a prolonged stalemate.

There was also the possibility that the landings could turn out to be a disaster for the British, but the official said that was not the view of American experts, a number of whom expressed confidence that the British would do well, at least in the short term.

The official, who asked not to be identified, said there were two crucial factors now that would require finding a new approach in order to reach a peaceful settlement.

One was that the commitment of major forces by both sides meant that anything could happen, that the momentum of the battle now made things unpredictable. The other was a question of whether the Argentine junta was capable of reaching a decision for a compromise negotiated solution under changed military circumstances if and when one side begins to gain the upper hand.

Ultimately, he suggested under questioning, there will have to be a political settlement, because the British, even if successful in retaking the islands, cannot stay and protect the islands forever.

The British landings also raised long-range questions for Washington and the North Atlantic alliance that are under intense study in the White House. The gravest problems could come if the battle is inconclusive and Britain faces long-term supply difficulties and continuing casualties or if so many British ships are sunk that troops on the islands cannot leave.

In its statement yesterday, the White House said any British requests for assistance "will be carefully evaluated on a case-by-case basis" while the United States continues to press for a peaceful solution.

American officials said yesterday that the British appeared to have landed possibly as many as 2,500 troops. But they also indicated that the bulk of the British ground troops sent to the South Atlantic still had not reached the region, suggesting that yesterday's landing was not an all-out invasion.

It is the battle in the air, however, that may ultimately be crucial because Argentina has a considerable numerical edge in air power. Based on reports reaching here yesterday, officials said it appeared that the Buenos Aires regime had thrown everything it could get into the air at the British fleet trying to protect the troop landing.

Until now, Argentina has been reluctant to commit its air force. According to British reports, the Argentine planes damaged five British vessels, two seriously.

This could tempt London to bomb airfields on the Argentine mainland to try to reduce the threat to the limited number of ships the British can deploy to the South Atlantic. Such bombing would be a "very significant step," as one top official here put it, meaning a major and dangerous escalation of the fighting.

On the other hand, the Argentines suffered heavy lossses in the air, including nine of the 21 front-line, French-built Mirage jets in their arsenal and five of their 68 U.S.-built Skyhawk jets. Thus, Argentina's first full-scale outing of its air force was costly and could make Buenos Aires think twice about exposing it again.

Although details reaching here were scarce, officials said it appeared that the British forces had landed on West Falkland Island, where, by U.S. estimates, some 1,500-2,000 Argentine defenders are scattered along the coastline.

The bulk of the defending force--variously estimated at between 7,000 and more than 10,000 troops--is concentrated around the main settlement of Stanley on East Falkland.

In order to support the landing in the west, however, the British fleet had to move its ships closer to the Argentine mainland. This brought the vessels within range of Argentina's main military strength--its air force based on the mainland.