Libya claimed yesterday to have shot down three U.S. warplanes that had violated the airspace over its waters and, in a broadcast last night, threatened to "strike mercilessly" with its missiles against the American 6th Fleet and "make the Mediterranean into a sea of fire."

In Washington, however, the Pentagon said no U.S. planes had been lost.

In bulletins on its state television, radio and news agency, monitored in Europe, and in a message delivered to the United Nations, the militant North African Arab state outlined its charges against the United States and its intention to continue what it called its "struggle."

The few reports from foreign correspondents in Tripoli yesterday gave no indication of unusual tensions, however, despite the reported rocket and missile exchanges at Surt, 225 miles east of the capital.

Doug Tunnell, of CBS, said that while security had been bolstered around Qaddafi Barracks, the main troop installation in Tripoli, the Green Square in the heart of the capital was lighted normally, and there was no outward sign of tension or imminent danger.

A Soviet ship was moored in the harbor, fully lighted, Tunnell reported, and there had been no mention on television in Tripoli of any Libyan or Soviet casualties.

Tass, the Soviet news agency, carried a brief report from Tripoli that merely repeated a statement by the Libyan news agency that "American Navy planes bombed a civilian vessel, but the bombs missed the target," The Associated Press reported from Moscow. Tass, in a report from Washington, said that "an American battle group, concentrated off Libya, has opened fire on the Libyan coast" while engaged in "provocative maneuvers."

A briefing to American pool journalists aboard the U.S. aircraft carrier Saratoga, 155 miles north of the Gulf of Surt, early yesterday afternoon gave no indication of attacks, AP reported.

Cmdr. James A. Harness, a 6th Fleet spokesman, told the reporters: "Libyan air and surface activity has been relatively light. There has been no evidence of hostile reaction by Libyan forces."

Earlier in the seven-hour visit by the reporters, Vice Adm. Frank Kelso, commander of the 6th Fleet in the Mediterranean, said that the U.S. forces involved in the maneuvers currently under way in the gulf planned to stay in international waters and airspace "as recognized by our country" and "by most of the countries throughout the world."

The Libyan television bulletin, monitored by the British Broadcasting Corp. in London and carried by the AP, said, "Brothers and sisters, we now received the following:

"The American Air Force commenced this morning violating the airspace over Libyan territorial waters in the Gulf of Surt. Our air defenses combatted and shot down three aircraft, two of which were shot down at noon and the third this evening. The three aircraft fell into the sea. "At about 1:20 p.m. the American fleet shelled the suburbs of the city of Surt using rockets."

The announcement ended with, "Al-Fatih forever, and the revolutionary struggle will continue." Al-Fatih means "the conqueror" -- an apparent reference to Libyan leader Muammar Qaddafi.

A similar statement was telephoned to ANSA, the Italian news agency, by the correspondent in Rome for JANA, the official Libyan news agency. It said, "American air forces from the 6th Fleet today launched a missile attack against the Surt Gulf region. Libyan air defense forces responded to the attack by shooting down three American fighter planes."

At the United Nations, Libyan Foreign Minister Kamal Hassan Makhour, in a letter delivered to the General Assembly shortly before the action yesterday, had warned that Libya would use force against U.S. planes and ships that it found violating its territory.

Kamal, according to an unofficial translation of his letter, condemned the "repeated military maneuvers by the U.S. government in front of the Libyan shores," and cited the "repeated threats of aggression by the United States against the sovereignty of the land and territorial waters of Libya," which, he said, create a threat to peace "in the region and all the world."

Because of these maneuvers and the results that might ensue, the letter said, "Libya may be obliged today to implement Article 51 of the U.N. Charter."

Vernon Walters, the U.S. ambassador to the United Nations, said in response to a question that he had told the U.N. secretariat of the U.S. action and intends to follow up with a letter protesting the Libyan missile attack.