An estimated 2,000 Libyans chanting support for Iran marched on the U.S.Embassy in Tripoli early yesterday then broke down the door and set fire to furniture as 14 Americans and others inside escaped unharmed through a side door.

The mission was the third U.S. Embassy in a Moslem country to be invaded in less than a month, following the Nov. 4 seizure in Tehran and an attack that destroyed the embassy in Islamabad, Pakistan, Nov. 22.

State Department spokesman said the first floor of the four-story building was "destroyed" by fire, and the second floor was "damaged." They said Libyan authorities had made no attempt to disperse the demonstrators or protect the mission despite repeated appeals by embassy officials during the hour-long attack.

Spokesman Hodding Carer said yesterday that the United States has protested "in the strongest terms" the "inadequate and unresponsive nature" of the reaction of the Libyan government, with which Washington has had difficult relations over the past decade.

U.S. appeals for additional embassy security were made to a number of counries with majority Moslem populations following the attack in Pakistan, including an additional request to Libyan authorities as recently as Saturday, Carter said.At the time of yesterday's assault, however, he said, only one local policeman was posted outside the Tripoli embassy.

The attackers eventually were dispersed by an automatic tear gas security system. Libyan government radio later charged that a number of demonstrators had been hospitalized from the effects of "poisonous gases" used against them by the embassy staff.

Asked if the attack had the backing of the government of Libyan leader Col. Muammar Qaddafi, State Department officials said Libya is not a country where "spontaneous" demonstrations are premitted, and indicated a belief that the government had "active knowledge" of the demonstration.

In a briefing early yesterday, Carter said the demonstrators included "a large number of people who go under the name of 'militia,' which would be . . . people who work in the [government] oil fields and the like."

Other State Department officials speculated that a downtown rally where the march began may have been goverment-authorized but got "out of hand."

Libya supplies 10 percent of U.S. oil imports at an annual cost of $6 billion, and is the third largest U.S. source of foreign oil. Libya also purchases approximately $450 million worth of U. S. export market in the Middle East after Saudi Arabia.

The Qaddafi government is among the most radical in the Islamic world, however, the relations with Washington have been strained since Qaddafi overthrew King Idris in 1969.

While he has called repeatedly on Iran to release 50 American hostages held in the U.S. Embassy in Tehran, Quaddafi has expressed strong support for the Iranian regime led by Ayatollah Ruhollah Khomeini. Libya is among the few nations to have said publicly it would aid Iran in the event of a U.S. attack.

In an early morning briefing yesterday, State Department spokesman Carter said the Tripoli attack began at approximately 10 a.m., Libyan time, (3 a.m. EST) when an anti-American rally in a downtown square began moving toward the embassy.

Carter said Secretary of State Cyrus R. Vance was informed of the incident at 4:30 a.m. and telephoned President Carter before arriving at the office at 5 a.m.

When a few demonstrators passed by the embassy, he said, two embassy employes walked to the square and return to advise the others to leave.

As the demonstrators reached the door of the embassy, an unfenced building on a narrow streeet, those inside "destroyed classified materials" and began evacuating through a side door. The demonstrators eventually "rammed" through the front entrance, Carter said.

At the time of the attack, Carter said, all 12 U.S. diplomats stationed at the mission were inside, along with the wives of two staff members, one visitor and six Libyan employes. Although Sunday is a normal working day in the Moslem country, he said, the doors of the embassy were locked as a security precaution.

By request of the Libyan government, no U.S. Marines are stationed at the embassy, which Carter said is a "full" diplomatic mission although its highest ranking officer is Charge d'Affaires William L. Eagleton rather than an ambassador. He said "between 2,500 and 3,000" Americans live in Libya.

The Libyan news agency later described the incident as a "tumultuous student demonstration held in solidarity with Iranian students and the Moslem Iranian people's revolution which is confronting imperialist and colonialist provocations and designs."

The agency report made no mention of an attack on the embassy but said that "upon the students' arrival at the U.S. embassy, slogans broke out calling for an end to American and imperialist hegemony, and affirming solidarity with the Iranian people."

The level of U.S.-Libyan relations was lowered in 1973 because of tensions over Libyan control of U. S. oil firms then operating there and Libyan objections to Mediterranean overflights of U.S. military aircraft. In May 1973, a U.S. diplomat stationed in Tripoli was refused readmittance to the country because his passport was not written in Arabic, according to new local law. Another U.S. diplomat was expelled when he protested the exclusion.

In June 1977, the mercurial Quaddafi praised Carter as "a good, religious man." The United States responded that it was willing to strengthen ties, but that Libyan support of terrorism and lack of cooperation on Middle East problems were "obstacles."