The Lebanese Army barely repulsed a strong attack on a strategic position near the capital early today, raising concern here that Syrian-backed forces were trying to link up with Moslem Shiite militia for a drive against the government of President Amin Gemayel.

In vicious hand-to-hand fighting through the night, the commander of a 90-man company was dismembered with a hatchet. Thirteen of his troops were slain, 20 wounded and another 20 missing.

Western diplomats and military officials said they expected the artillery and ground battle for control of the Army-held town of Suq al Gharb--on commanding heights above the presidential palace--would resume.

These sources said the Lebanese Army has closed in on supply routes of its foes and that the attackers may be running out of ammunition. But they said the fledgling army was tired after two weeks of fighting, stretched thin and constrained by both logistical and political considerations from mounting any major offensive in the mountains. Gemayel's government was depicted as weary and apprehensive.

If Suq al Gharb falls, Beirut will be extremely vulnerable, the western officials said. The battle, the most intense assault on the Army yet, began early last evening and continued into the early hours today. Attackers overran a position of the company of a U.S.-trained battalion, regarded as the Lebanese Army's best, before being pushed back.

Lebanese Army spokesmen charged that the assault was carried out almost exclusively by Palestinians and Syrians, whose nationality they said Lebanese soldiers were able to determine by their accents.

The Army showed journalists three mangled bodies said to be the remains of attackers. The soldiers showed journalists two identity cards, one of a Syrian civilian and the other of a member of the Fatah faction of the Palestine Liberation Organization, that the spokesmen said had been found on two of the men.

Western diplomats and military officials, although skeptical of prior claims of direct Syrian involvement in the bloody, week-long fighting in the mountains, indicated today they were persuaded by the evidence presented by the Lebanese.

Western military officials also argued that Druze fighters, in the sustained drive against Christian Phalangists and their now open push against Army units in the mountains, did not have the manpower or logistical support to sustain the fighting as long as it has gone on and therefore must be relying now on outside help.

Druze spokesmen have previously acknowledged getting armaments and supporting artillery fire from Syrians occupying eastern Lebanon. They denied again today, however, that either Syrians or Palestianians were fighting alongside them. Journalists have seen Palestinian fighters in areas captured by Druze.

Since the Christian-Druze fighting in the mountains erupted into what is now being called full-scale conflict--following Israel's pullback last Sunday--Lebanese Christians and the government have directed a concerted campaign at American journalists to counter perceptions that the conflict is "civil war."

Joyce Gemayel, wife of the president, called an ABC-TV producer here today to say that she and her husband were very unhappy that President Reagan had used that term in a telephone interview with Republican officials yesterday. She said she had called U.S. Ambassador Robert C. Dillon to ask that he hold a press conference to correct the perception.

Later, journalists were summoned to a background briefing. The ground rules were that officials could be identified only as western diplomats and western military officials.

The Lebanese apparently perceive faltering U.S. public support for the presence of the U.S. Marines as they come under attack here. At the same time, the Lebanese are eager for the United States and other contingents of the multinational peace-keeping force to take on an expanded military role.

The issue arises as the Reagan administration prepares for controversy over the War Powers Act, with Congress coming back this week.

Some observers here forecast that when the Druze and their Syrian allies finish their apparent drive to take control of the mountains, they will link up with the armed Shiite Moslems at the base of the hills and near Beirut International Airport.

U.S. marines were in their foxholes again today for more than 90 minutes as mortar rounds fell. The first two shells fired this afternoon crashed inside the compound. The half dozen or so others appeared directed toward nearby Lebanese Army positions, indicating that the marines had not been the target. There were no casualties.

Members of the multinational force stepped up their activity in the past several weeks, although their stated role remained unchanged: providing a powerful presence while the Lebanese Army is rebuilt and the government here seeks to extend its authority over Lebanon. But Reagan has sent another Marine amphibious unit of 2,000 troops to be based offshore. The French recently brought in the aircraft carrier Foch.

Today, a pair of British Buccaneer jets brought to Cyprus last week swept over rooftops in Beirut and the mountains and U.S. F14 Tomcats were also in the air. A U.S. spokesman said the F14s were flying "tactical reconnaissance in support of the Navy and the Marines."

Reporters here saw four Israeli tanks and eight armored personnel carriers patrolling the coastal highway in Al Jiyeh, not far from the mountain fighting, in an area about six miles north of the Awwali River, the new demarcation line for Israelis after their pullback last week.

Washington Post correspondent Edward Walsh, in Jerusalem, said Israeli military officials described the patrol as a "local precautionary measure" because of the fighting in the area. "It was a small patrol. It wasn't enough to make anyone think we were moving north in force," an Israeli military official said.

Walsh reported that the Israelis appeared to be in a holding pattern, trying to gauge exact Syrian and PLO roles in the areas Israel vacated. If Syrian troops move in force, the official said, there would be a "reassessment" of the current Israeli stance. There were reports in Israel that Defense Minister Moshe Arens had been in Lebanon today.

U.S. envoy Robert C. McFarlane was in Beirut again today as part of his continued shuttle diplomacy to obtain a cease-fire and reconciliation among the various Lebanese factions.