The U.S. military today turned over security duties in this seaside capital city to a small Caribbean force as American troops continued to fight against what they said were an estimated 500 Cubans holding out in parts of the island.

As the first contingent of the joint Caribbean Security Force arrived, both the U.S. military commander and the chief of the Caribbean nations force predicted that U.S. troops would have to remain in Grenada for some time to come.

"How long we continue operations here is a factor of how long the Cubans want to fight," said Admiral Joseph Metcalf III, commander of the U.S. joint task force that landed on Grenada four days ago. In an interview with a pool of 26 foreign journalists at the Cuban-built airport at Point Salines south of the capital, Metcalf said: "If the Cubans want to play games and go into those hills it will take quite a while [to end military operations]."

Col. Ken Barnes of Jamaica, the Caribbean Security Force commander, predicted the United States would not be able to leave Grenada "before a matter of months."

While his force would now take over security in the capital, Barnes said, his men are not trained to fight the snipers thought to be in the city and in the hills beyond it.

Barnes made his comment here minutes after U.S. Marine Corps Blackhawk helicopters landed 250 of his 300-man force in Grenada at the Queen's Park cricket grounds.

There was no official handover ceremony, and Barnes' men marched off the cricket grounds into the city immediately after landing, behind two U.S. Marine Corps amphibious armed personnel carriers.

The decision to leave the security of the capital city to a force of about 250 soldiers and police from six Caribbean nations was designed to underline the allies' participation in the military occupation of the island.

The city was calm today, despite the evidence of recent bombings, looting and a fire in at least one police station.

But there were signs that the fighting on the island was still not over after four days of U.S. military operations.

Journalists saw evidence of continued military clashes on the outskirts of the capital as well as in the densely vegetated mountainous interior of this small island.

Witnesses said that U.S. Rangers from the 82nd Airborne Division were still fighting against elusive bands of snipers in and around the holiday beach hotel strip along the Grand Anse Bay, just south of the capital.

The sounds of battle were also heard throughout the afternoon just east of the still-uncompleted air strip at Point Salines.

The air strip, which the Reagan administration claimed was being built not for the commercial traffic as the Grenadan government insisted but as an important strategic military base for Cuba and its Soviet sponsors, has been the main staging area for the U.S. military force.

Metcalf said the force had now reached about 5,000 men on the ground and another 10,000 men afloat with his battle group off the Grenadan coast.

[In Washington, the Pentagon said more than 6,000 U.S. troops are participating in the invasion, including 5,000 from the 82nd Airborne, 500 Marines, several hundred support personnel and the Rangers already stationed on the island.]

In the rolling hills just a few miles off the air strip's 5,000 foot-long runway, the odd crump of outgoing mortar fire could be heard intermittently throughout the afternoon.

Overhead, a gray C130 Spectre gunship circled into the night, firing occasional deep-throated salvos from its awesome rapid-fire 100mm howitzers.

Journalists, escorted by Rangers to view a cache of captured Grenadan arms and ammunition in a group of corrugated tin warehouses about a mile from the airport, saw a Ranger platoon deployed in a perimeter defense position just beyond the warehouses.

The soldiers, their young faces smeared with green camouflage paint, crouched in ditches along the road, their guns pointing east into the hilly tropical brush where the sounds of gunfire could be heard. Behind them, in a truck park, a row of 80mm mortars had been mounted to provide protective covering fire if necessary.

Along the road back to the airport, less than a quarter of a mile from the runway, the body of a dead man in civilian clothes was lying on its back under a canopy of a frangipani tree. Both legs had been blown off below the knees and the torso had begun to darken and swell in the stifling heat of a tropical sun.

According to the U.S. Rangers, the man was believed to have died Thursday evening when an air strike by two U.S. Navy A7 Corsair carrier-based fighter bombers were called in to blow up a concrete house where snipers were believed to have holed up. The house was demolished, but whether the snipers were ever found could not immediately be established.

Metcalf, a feisty and slight naval officer in gold-rimmed eyeglasses, insisted that "organized resistance" on the island had in fact already ceased.

His men, he said, were now just conducting a "bush operation of light fighting" to flush out snipers who continued to make large parts of Grenada unsafe.

"Sniping is going to be a continuing problem," Metcalf said. "It has been a problem all along. They are still shooting at us but we have been lucky because they are bad shots."

Metcalf said the United States was able to set the number of remaining Cubans at about 500 through information provided by captured combatants.

The admiral said the number of Cubans was higher than expected, one reason why the U.S. felt the need to increase the level of its own forces. Asked whether that meant that U.S. intelligence had been faulty, Metcalf snapped: "I don't know, I'm not an intelligence officer. Let's just say it wasn't adequate."

Metcalf spoke with journalists from a press pool who had been flown here from Barbados for a five-hour guided visit.

The inverview was held in the still-unfinished airport terminal building before the troupe of journalists was taken by helicopter over sniper-threatened roads north to St. George's.

The admiral referred all questions about the total number of U.S. casualties during the operations to Defense Department spokesmen in Washington. These spokesmen today gave the U.S. casualty toll as 11 dead, seven missing and 67 wounded.

Metcalf said however that his men to date had killed 36 Cubans or Grenadans who had resisted the U.S. advances.

He gave the number of wounded enemy combatants as 56. Metcalf said his men had had no chance to break down this casualty figure by nationality. But he said he thought most of the resistance came from Cubans rather than Grenadans loyal to the island's now-toppled Marxist Revolutionary Military Council.

Despite the dead body of an unarmed man lying near where goats grazed and yellow butterflies flitted over purple bougainvillea flowers, Metcalf said there had been no civilians killed since his force of U.S. Marines and Rangers assaulted the island in a two-pronged helicopter attack shortly after dawn Tuesday.

The admiral said that of the now estimated 1,100 Cubans believed to have been on the island at the time of the U.S. landings, almost 650 have now been captured and more are either giving themselves up or being captured by the hour.

[The Pentagon today said 638 Cubans and 17 Grenadans had been captured.]

How many of those captured were combatants no one in the U.S. command here seems to know for sure.

Cuba has insisted all along its men were mostly construction workers laboring on the airfield while the Reagan administration has alleged they were almost all armed members of an engineering battalion there not only to work on the airstrip but to help defend the island's pro-Cuban regime.

Just above the airport, on a hill dotted with ramshackle wooden barracks that once housed the Cuban workers, a prisoner of war center now holds more than 500 Cuban prisoners, according to a U.S. Ranger officer.

At least 200 of them were in three pens surrounded by razor-sharp rolls of concertina wire laid out on an asphalt parking lot between the barracks.

The men looked relaxed and were all dressed in civilian clothes. Most wore straw hats or had bandanas tied around their forehead. Many joked among themselves while smoking long Cuban cigars. Most were either squatting or stretched out on small cotton mattresses that had been stripped from their barracks.

The only Cuban who could be interviewed through the wire before U.S. military officials forbade any talking to the prisoners said his name was Fulgencio Gonzalez Molina.

"We are noncombatants here; we are just laborers," he said through the wire enclosure. "I was just a cook here, not a fighter."

Chief Warrant Officer Rolf Milton, the 37-year old Ranger in charge of the prisoners, said all of them were Cubans and most had come from the airport area. "Which are active combatants we really don't know," Milton said, "not one of them has admitted to being a soldier."

A Ranger officer showed journalists through the Cubans' barracks which had been looted and rifled. Family photographs of wives and children back in Cuba, personal letters, Cuban political magazines extolling Marxist-Leninism, clothes, assorted shoes and boots, and other personal effects, were scattered over the floors.

Outside the barracks, Ranger officers pointed out half a dozen shallow rifle trenches as proof that the Cubans had planned to resist from their barracks -- although there were no signs of any fighting having taken place in the immediate area.