U.S. Marines and paratroops backed by helicopter gunships appeared tonight to have overrun most major positions held by Cuban forces in Grenada, but scattered resistance continued elsewhere in the Caribbean island.

About 800 paratroops from the 82d Airborne Division were airlifted into Grenada to reinforce about 1,900 U.S. troops already there as they cautiously fanned out from two airports seized in a surprise attack early yesterday morning, according to U.S. and Caribbean officials.

President Reagan said he ordered the attack to protect about 1,000 U.S. citizens on the island and in response to a request from neighboring Caribbean states fearful of the turmoil following a coup there. Because no journalists have been able to send information from Grenada, most of the information available about the fighting there has come from official U.S. sources, the government-controlled Cuban media or the governments of neighboring Caribbean states.

Secretary of Defense Caspar W. Weinberger said at a Pentagon news conference that six U.S. servicemen had been killed in the fighting, 33 had been wounded and eight were missing.

At the news conference, Gen. John W. Vessey Jr., chairman of the Joint Chiefs of Staff, said the operation was "successful so far" but that "we encountered a lot more resistance than we expected" in the action on the 133-square mile island.

The Cubans were reported to have lost at least 12 dead, with Havana reporting that its soldiers had fought to the last man at some positions. There was no word on Grenadan military casualties but Barbados state radio said 18 Grenadan civilians had died. At midday a C141 jet transport took off from one of the captured airfields carrying the first American civilians to a military installation near Charleston, S.C. Other evacuation planes followed.

Cuban media said six U.S. helicopter gunships pounded Cuban positions this morning, destroying a building the Cubans held and causing "numerous" casualties. Cuban media later reported that Cuban forces had ceased resistance.

But Weinberger said tonight that Cubans were continuing to harass the invading forces. Weinberger made no prediction as to when all resistance would be snuffed out, but U.S. officials continued to say they hoped the American troops would be able to leave soon.

Weinberger said about 600 Cubans had been captured and that some of the Cuban wounded were being treated on the island and on the aircraft carrier Guam. State Department spokesman Hughes said all Soviet personnel on the island are "in their diplomatic buildings and have not ventured out."

Even as the two top military officials spoke at the Pentagon late yesterday, after a day of official silence, an aide handed Vessey a note saying that one of the two remaining pockets of resistance had been taken.

Vessey said U.S. forces captured the Grand Anse campus of the St. George's University School of Medicine on the southern end of the island and evacuated all its students in at least six helicopters. About 650 Americans attend the medical school.

Fighting continued between U.S. forces and Cuban and Grenadan combatants at Richmond Hill, just east of the capital of St. George's, the site of an island prison where Weinberger said political prisoners may still be held. Vessey also said that additional pockets of resistance may be encountered as U.S. forces try to consoldiate their control over the island.

Grenada's Governor General Paul Scoon, Queen Elizabeth's ceremonial representative in Grenada, a Commonwealth state, was flown to the U.S. aircraft carrier Guam. The Defense Department said U.S. forces rescued him from Grenadan soldiers who had surrounded his house.

State Department spokesman John Hughes said the United States viewed Scoon as the "legitimate constitutional authority" in Grenada and hoped he would form an interim government pending elections. The fate of Gen. Hudson Austin, who seized power in a bloody coup that killed former prime minister Maurice Bishop and several other government officials last week, remained uncertain.

A spokesman for the government of Barbados said Deputy Prime Minister Bernard Coard, believed to have been behind the coup against Bishop, had spoken on Grenadan radio at the beginning of the invasion. The spokesman said: "Our assumption is that Coard has taken refuge in the Soviet Embassy."

Austin's coup prompted the invasion by U.S. Marines and paratroops. About 400 troops from six Caribbean states--Antigua, Barbados, Dominica, Jamaica, St. Lucia and St. Vincent--were flown in after the airports were secured, bringing the total number of troops in the invading force to 3,000. Reports in Barbados yesterday indicated that the Caribbeans were being limited to guard duty in areas cleared by the Americans. Radio Barbados reported that there were no casualties among the Caribbean units.

Most of the fighting yesterday was near the St. George's capital and south of it, officials said at the Pentagon news conference. Vessey said U.S. forces met "organized resistance" from mostly Cuban forces, although Grenadans were apparently also engaged.

The two biggest battles were at the "beach campus" of the medical school at Grand Anse and at Richmond Hill. Both sites presented difficult problems for U.S. forces, officials said, because they did not want to injure or endanger the students and prisoners inside the disputed buildings.

The medical school was captured without injury to students late in the day, and officials said that once Richmond Hill--with political prisoners possibly inside--was taken, all major objectives would be secured.

Weinberger said he could not provide Cuban or civilian casualty figures, but Vessey said 20 of the 600 captured Cubans were wounded. He said they were being treated by Cuban doctors, and that the prisoners were being handled according to the Geneva Convention, although the United States is not at war with Cuba.

Pentagon sources said they believed Cuban "senior military advisers" and other personnel arrived in Grenada several days ago in anticipation of possible U.S. military action.

Pentagon officials said U.S. fighter jets from the decks of the carrier Independence maintained a "combat area patrol" to watch out for Soviet and Cuban fighters that might threaten the operation, but saw no signs of a challenge. The Independence and its battle group operated mostly on the west side of the island, while the amphibious landing group that transported the Marines was to the east.

As facilities were taken by Rangers or Marines, regular Army troops from the 82d Airborne Division moved in to hold their gains, officials said.

Officials said Navy Seals had also been involved in the early stages of the invasion. The elite forces landed in small boats to infiltrate behind enemy lines hours before the arrival of Marines and Army Rangers.

The invasion, the first U.S. military operation in the Caribbean since U.S. forces intervened in the Dominican Republic in 1965 is being supported by about 20 ships standing off the coast of Grenada which lies about 90 miles north of Venezuela.

Barbados' Grantley Adams Airport has been transformed into a bustling forward supply base. At midday today 10 Marine transport helicopters, two observation helicopters, about 12 C130 transports, a giant C5 Galaxy jet transport and at least two AC130 Spectre gunships were seen at the airport.

U.S. servicemen loaded pallets of cargo, supervised refueling and stood guard with M16 rifles.

Weinberger said more troops were available as reinforcements--presumably both Marines offshore and soldiers in the 82d at Fort Bragg, N.C.--but he said he did not believe more troops would be needed.