The Lebanese Army appeared to be stalled today in efforts to strengthen its control over the vital heights above the presidential palace and capital against Druze and Palestinian combatants as fighting here entered its third week.

Reporters who visited the battle scene around the Army-held strategic heights in the vicinity of the town of Suq al Gharb said the Army was moving only slowly and that the tired units appeared to be suffering heavy casualties.

The situation was tense here today between the United States and Syria after U.S. naval ships fired for the first time yesterday into Syrian territory in Lebanon's Upper Metn mountains.

The Associated Press reported that official sources in Damascus said Syrian President Hafez Assad had ordered his forces in Lebanon to retaliate against any American air, sea or land bombardment.

Operating under President Reagan's new instructions, the naval ships fired at the Syrian positions after the Lebanese Defense Ministry, where U.S. military advisers have offices, and the U.S. ambassador's residence in the eastern suburbs of Beirut again came under heavy shelling yesterday.

Spokesmen here said the shelling diminished after the warships fired but did not stop.

The Navy did not fire its guns today, according to Marine spokesman Maj. Robert Jordan. But U.S. Navy F14 Tomcat fighter planes made "routine reconnaissance" flights, he said.

Marines received sporadic small-arms fire and returned it with small-arms fire, Jordan said, but no one was injured.

The Lebanese Army also was the target of ground attacks in the tense southern slums of the city. Local radio stations here blamed pro-Iranian Shiite Moslems.

The radio stations also broadcast unconfirmed reports of another massacre of Christians. This one was said to have occurred in the town of Majdalaya, south of Suq al Gharb. State-run Beirut Radio said 13 persons were killed. Christians and Druze have accused each other of massacres almost daily in recent weeks.

There was also continued shelling of Christian suburbs of the capital, including areas near a makeshift landing strip on the coastal highway that was built by the Lebanese Army during the past week so that it could fly fighter planes. The reports were that five civilians had been killed in the shelling.

In other developments, The Associated Press reported:

Lebanese police and witnesses said artillery fire from Syrian-held northern Lebanon struck Christian targets in the port of Byblos, 23 miles north of Beirut, for the first time in the current fighting, as well as neighborhoods in Christian-populated east Beirut.

The police said dozens of shells and rockets slammed into vehicles and damaged buildings, killing at least 16 civilians and wounding 42.

Three Lebanese government Hawker Hunter jets strafed and rocketed Druze militia and Palestinian positions near Suq al Gharb, reporters in the battle zone said.

They said the Lebanese Army also pressed efforts to flush Druze and Palestinians out of towns and villages on either side of the ridge, but that antigovernment snipers remained in zones already taken by government soldiers.

Two members of a British television news crew were reported wounded, apparently by rebel shrapnel.

President Amin Gemayel, in a television interview on "This Week with David Brinkley" (ABC-WJLA) said his government is seeking a political solution, but reconciliation with the Druze was being blocked by Syria.

He was asked if he thought the U.S. Marines would fight alongside his Army, and he replied, "I don't think that will be necessary. We are pushing a political initiative for a political agreement."

In a television interview broadcast in Paris, Gemayel said that Palestinian guerrillas trying to regain a foothold in his country are the Lebanese Army's principal enemy. Asked if he regretted the pullback by Israeli forces because it had allowed an advance by Syrians and Syrian-backed Palestinians, Gemayel said, "That is the reality of the fight that the Army is conducting at the moment."

In Tripoli, Libya, the official news agency JANA reported Libyan leader Muammar Qaddafi ordered his troops in eastern Lebanon's Bekaa Valley "placed under the disposal" of Druze leader Walid Jumblatt.

Libya is believed to have about 300 troops in the Bekaa. But there has been no indication they have been involved in the fighting so far.