Britain said its ground forces, advancing against heavy fire, captured Darwin and the strategic Goose Green airstrip yesterday, as the war in the Falkland Islands shifted into a new and potentially more bloody phase.

British Defense Ministry spokesman Ian McDonald announced last night that paratroopers had overrun Argentine troop concentrations at the two key sites, 17 miles south of the British beachhead at San Carlos. He gave no estimate of British or Argentine forces involved in the attack, the first major ground combat in the South Atlantic conflict, but sources in London put the Argentine total at fewer than 500.

"The Argentine forces suffered casualties and a number of prisoners have been taken," McDonald said. "Initial reports are that Britishcasualties are light."

Argentina's military high command in a communique denied the British claim. It said its troops had launched a counterattack yesterday morning that had driven back the British assault, which it said began before dawn with support from heavy naval bombardment.

"Our aviation neutralized the fire from the British ships and Argentine Army troops, supported by planes, forced the enemy back, totally recovering the territory, controlling the tactical situation and obliging the enemy to retire toward the north," said the communique from Buenos Aires. It said helicopter-borne British troops then launched a second offensive to take the area and "action continues at present."

A later communique said Argentine forces shot down two British helicopters and damaged one frigate in fighting at Darwin.

Neither side reported casualty figures for yesterday's fighting. But the British Defense Ministry said a series of Argentine air raids Thursday on San Carlos had killed four Royal Marines and wounded about 20 others. The ministry reported that two Argentine Skyhawk warplanes were downed in the raids, and that a British Harrier jet was shot down over Stanley, the Falklands capital and the ultimate objective of British forces.

As the fighting appeared to continue moving toward a climactic ground battle, diplomatic efforts to resolve the conflict continued. At the United Nations, Secretary General Javier Perez de Cuellar met with Argentine envoy Arnoldo Listre in the third day of new talks seeking a cease-fire.

In Washington, Latin American foreign ministers at the Organization of American States adopted a resolutiondemanding an immediate end to Britain's "unjustifiable attacks" and a halt of U.S. aid to Britain.

Anticipating that demand, President Reagan in a speech in Santa Barbara, Calif., appealed to the Latin American states not to allow their sympathies for Argentina to harm their good relations with the United States. "Let's make certain that emotions don't blur the truth of how close we really are during this tragic conflict," Reagan said.

British sources said the reported capture of Darwin and Goose Green gives their ground troops three tactical advantages: it eliminates an Argentine threat to the flank of British troops as they move toward Stanley; it gives the British control over the only road, a clay track, that crosses East Falkland Island without interruption, and it gives them the second-best airstrip on the island after the one at Stanley.

Argentine military analysts also conceded that the loss of the twin settlements would leave Argentine forces with only Stanley as a defensive stronghold with extensive artillery and fortifications. The loss would also indicate that Argentina had failed to contain the British landing force at San Carlos, where British paratroopers and Royal Marines first landed a week ago.

Both sides offered few details of yesterday's fighting. Britain earlier had reported only that "offensive land operations" were under way and that both sides had suffered "a number of severely wounded casualties." Sources in London said large numbers of troops were advancing not only toward Darwin and Goose Green but also toward Stanley, about 50 miles east of San Carlos, where at least 5,000 Argentine troops are believed to be dug in.

In London, a news blackout prevailed again through most of the day and even government ministers received relatively little information. British correspondents with the forces on East Falkland have not been able to send any reports to London for two days.

But the British Broadcasting Corp. reported that Royal Marines with Scorpion light tanks and artillery had moved directly east from the San Carlos beachhead toward Stanley in a thrust apparently aimed at gaining the high ground overlooking the capital. The Argentine defenders reportedly are entrenched in a wide arc said to stretch from Green Patch to Bluff Cove.

The British Defense Ministry refused to confirm this account. But it provided a few details of Thursday's wave of Argentine air attacks.

The ministry said Argentine Mirages and Skyhawks bombed and strafed Royal Marines on the ground around San Carlos. It added that the two Skyhawks were shot down by antiaircraft fire from the British ground base.

During the air raids, a British hospital ship, the converted cruise ship Uganda, was brought into Middle Bay, just north of the inlet of San Carlos, for 30 minutes to pick up both British and Argentine casualties requiring intensive medical attention. The Defense Ministry denied that the Uganda participated in hostilities, but Argentina's military high command repeated its charge that the ship was being used for miltary purposes and warned it could be subject to attack if not removed from the war zone.

Through yesterday afternoon, sources in London said, there still appeared to be no significant Argentine ground troop movements. Their forces apparently remain dug in waiting for the British attack and leaving any counteroffensive to Argentine warplanes, the sources said.

A senior British government source said that before beginning their offensive, the British forces managed to get "an enormous amount" of equipment, food and other supplies safely ashore from task force ships despite Argentine bombing raids. Despite the loss of five ships and damage to others, he said, British forces were nowhere near in danger of losing the 25 per-cent margin of arms and equipment brought to cover losses.

Argentine military sources, in contrast, sought to portray British land forces as running low on supplies and ammunition due to constant pounding by Argentina's warplanes. The planes would continue taking a heavy toll of British ships, an Argentine naval spokesman told the official news agency Telam.

"The colonialist fleet may be in for another surprise from our aviation at any moment," he said.

The British have reported losing 109 dead so far in the conflict, which began when Argentine troops seized the islands April 2. Argentina acknowledges 92 dead and 309 missing, including 301 seamen missing and presumed dead in the sinking May 2 of the cruiser General Belgrano. Military analysts on both sides have said they expect the death toll to mount rapidly as ground forces, armed with sophisticated weapons, engage in battle.