Syrian peacekeeping forces pounded Christian districts in east Beirut with random artillery and rocket fire yesterday in the second day of heavy fighting between the Syrians and rightist Christian militias they formerly supported.

Residents said it was the worst shelling in Beirut since the 1975-76 civil war, which ended in late September of 1976 when troops from neighboring Syria moved in on the side of the Christian rightists against a Moslem, leftist-Palestinian alliance.

The shelling, which started in late afternoon, continued into the night in defiance of an 8:20 p.m. cease-fire deadline reportedly arranged with Syrian authorities by Lebanese President Elias Sarkis.

Two main targets of the Syrian guns were the headquarters of the Phalangist Party and the National Liberal Party, both of which are Maronite Christian groups that field large militias. Both buildings came under heavy shelling that set them on fire.

The main casualties in the fighting were civilians living in the Christian Ashrafiyeh district, rightist sources said. They had no firm casualty figures but estimated that scores of people may have been killed by the Syrian shelling.

Christian resident huddled in basements or at the bottom of their stair-wells as artillery, mortars and rockets landed without pause, setting many buildings on fire.

Rightists said that Christian militias were fighting back with sniper fire.

Yesterday's fighting started 24 hours after a clash Saturday in which Syrian shelling of the Christian Ain Rummameh suburb southeast of Beirut took at least took at least 22 lives and left 88 people wounded. Followed several days of tension between the Syrians and Christian militiamen since 400 gunmen killed more than 30 Phalangist sympathizers in the eastern Bekaa Valley Wednesday. Villagers and Phalangist Sources blamed the attack on Syrian troops.

Sources in Christian East Beirut said the latest clash began when two Syrian soldiers were shot and killed in the Christian sector, but a Phalangist spokesman dismissed the report and charged the Syrian attack was unprovoked.

"Even if two Syrian soldiers were killed, it's not a reason to shell a whole population," the Phalangist official said in a telephone interview from his east Beirut home as explosions echoed in the background.

The Phalangist official complained bitterly that the Christian side contacted the U. S. embassy here last night to appeal for help but were told the parties should stop fighting on their own accord, "as if we were the ones who started it."

Syrian radio indirectly accused the rightists of starting the fight, saying, "Those who are causing trouble in Lebanon and attacking the Arab peace-keeping force should realize such attempts will be crushed without mercy."

Besides the Christian party headquarters, the Phalangist radio station was knocked out and the Beirut port demaged by Syrian shelling. At least one freighter was reportedly sunk when it took a direct hit.

By midnight the shelling had ended and only sporadic machine gun firing could be heard.

News services reported the following:

A dozen shells fell near Syrian positions in Moslem west Beirut. Palestinian officials said that a few shells had fallen in the refugee camp of Sabra.