The U.S. Embassy in Beirut came under mortar fire and two Marine guards were wounded yesterday as Syrian troops pursued their relentless drive to shell Lebanese Christian militias into submission.

One Marine Sergeant suffered internal injuries when the blast of a mortar round crashing into a garden in front of the embassy hurled him 20 feet, and a second was nicked by the shrapnel that sprayed the embassy entranceway, an embassy spokesman said.

The Syrian gunners pummeled Christian positions with increased fury despite Thursday night's shelling by Israeli gunboats, which Israeli officials said was intended as a warning to Syrian President Hafez Assad. Observers said the Israeli attack, which did little damage, may have had the opposite effect by angering Syrian artillery officers.

At least one Palestinian and three Syrians were reported wounded, however, and some Syrian artillery batteries were said to have been knocked out by the Israeli bombardment.

Unconfirmed reports circulated here that the Israeli shelling - which Jerusalem said aimed at a Palestinian guerrilla base - was designed to cover the landing of ammunition or reinforcements for the rightist Christian militias, partially cut off from their mountain strongholds north of Beirut.

The U.S. Embassy lies in Syrian-controlled western Beirut, beside the Mediterranean about a mile from the main Christian stronghold of Ashrafiyeh where heavy Syrian artillery barrages rained down. Western diplomats speculated privately that the mortars were fired by Christian gunners, perhaps, they said, to dramatize impatience with U.S. and other Western responses to their leaders' pleas for help.

The Voice of Lebanon, the radio of the Christian Phalange Party, said that if Washington does not act immediately to end the fighting, which has escalated sharply in the last week, "you will be declaring a cease-fire for a country that doesn't exist and a people that has perished."

A U.S. Embassy spokesman said one of the Marine guards and four other persons, including Lebanese embassy employes, were taken to a hospital.A dozen persons were injured by the blast, most of them slightly.

Several other mortar rounds exploded harmlessly in the sea and on shoreline rock across the street, but one round was reported to have hit the nearby East German Embassy.

Yesterday's mortaring was the first known shelling of the U.S. Embassy in the current round of fighting between Syrian troops and the rightist Christian militias. The embassy building was nicked by small arms fire several times, however, during the 1975-76 Beirut war between the Christians and an alliance of Lebanese Moslems and Palestinian guerrillas.

The Phalange radio quoted party estimates that more than 800 persons have been killed and 3,000 wounded since the Syrians launched their latest onslaught against the militias last weekend. Most of the victims have been Christian civilians.

The battles and fires started by shells left a dingy gray pall of smoke hanging over Beirut. The only light after the sun went down came from the flash of firing cannons and piles of rubbish burning on street corners.

Electricity was off except for homes with privates generators. Running water stopped in most buildings. Telephones and telexes were down most of the time.

Beirut airport, one of the few Lebanese facilities still working, also was without water and electricity. Its communications, too, were disrupted. But some flights were still arriving and departing in special landing and takeoff patterns to avoid the fighting.

Flights out were full of grim-faced Lebanese, some weeping.

"All of my relatives are in the mountains," sobbed Laure Khoury, a 24-year-old secretary fleeing for the nearby Mediterranean island of Cyprus. "They're shelling every day. I don't know if I will ever see them again - my parents, my brother and sister, their children."

The Phalange radio reported sharp artillery clashes in the Dahr Baidar and Dhur Shweir areas, at a key crossroads on the main highway linking Beirut and Damascus over which most Syrian forces and supplies move on the way to Beirut.

The Syrians, backbone of an Arab League force designed to impose peace on Lebanon's warring factions and the Palestinian guerrillas, also attempted to infiltrate into the Christian areas of Ain Rumanneh, Hadeth and Dikwaneh, the radio said.

The command of the 30,000 Syrian troops said the main fighting occurred near a bridge on a road from the beleaguered Christian quarter of Ashrafiyeh northward up the coast, where the rightist militias have in the past offloaded their arms and ammunition. Syrian artillery destoryed two World War II-vintage Sherman tanks that the Christians had launched against Syrian positions on the bridge, the command communique said.