Fighting described as the heaviest in nearly three years battered Beirut today and the Christian city of Zahle, 50 miles east of the capital, came under heavy shelling that reportedly killed and injured dozens of people.

In both cities, the heaviest fighting appeared to be between right-wing Lebanese Christian forces and the all-Syrian Arab Deterrent Force that has been in the country since the 1975-76 civil war.

Casualty figures were difficult to obtain, but various sources estimated that the day's fighting killed about 60 persons, including 27 in Christian East Beirut, and wounded 240.

At the height of the fighting in Beirut, the capital's international airport was closed and several cargo vessels left the harbor, which came under heavy shelling.

The reason for the sudden surge in fighting was disputed. Sources in the right-wing Lebanese Phalangist militia charged that the Syrians, joined by Palestinian and leftist Lebanese forces, had started the exchange by shelling Christian neighborhoods and refugee camps as a "diversion" to their efforts to bombard Zahle in the Bekaa Valley.

Damascus radio, however, blamed the increased fighting on the "Phalange gangs that are operating with evident backing from Israel."

The Bekaa plain, a fertile stretch of farmland between Lebanon's two mountain ranges that stretch parallel from north to south, is a passageway to beleaguered southern Lebanon and considered a strategic location because it makes that area accessible through roads other than the exposed coastal highway.

The Syrians are said by sources to be bent on securing this vital link through Zahle and placing a firm grip on the town. According to the Phalangists this reflects a decision made during a meeting between Syrian officials and the Lebanese National Movement, an alliance of leftist Moslem and pro-Palestinian groups, on March 19.

[In Tel Aviv, Israel's government-controlled radio quoted Deputy Defense Minister Mordechai Zippori as saying that Israel "will not stand quiet if there is a threat to the Christian community" in Lebanon. Israel used similar expressions of concern for Christians to explain its 1978 invasion of southern Lebanon.]

Relations among the Lebanese left and right, the Syrian forces and the Lebanese government have been tense since the cease-fire that ended the civil war, but there had been no fighting on a scale comparable to today's since 1978.

Tension along the line separating Christian East Beirut from the Moslem western portion subsided somewhat tonight after fierce exchanges of artillery fire this morning.

Hospital sources quoted by Christian Phalangist officials put the toll in East Beirut at 27 dead and 128 wounded. Palestinian sources said 15 people were killed in West Beirut's predominantly Moslem quarters as a result of the violent battles across the capital's hot dividing line, a flash point for recurrent flare-ups during the last two weeks.

The Palestine Liberation Army, the Palestinian contingent of Syria's Army deployed in Beirut's commercial district and western section, traded fire with East Beirut Christian militias under the command of Phalangist militia chief Bashir Gemayel.

Residents of East Beirut said in telephone interviews that many families fled with packages of belongings when it was broadcast on Phalangist radio that Lebanese President Elias Sarkis, officially the supreme commander of the Arab Deterrent Force, had called for a cease-fire. Accounts differed on whether it was an official order or a plea, but in any case, it went unheeded.

At 10 p.m., Beirut radio quoted a Defense Ministry spokesman as saying Lebanese Army positions at a main east-west crossing here, as well as a nearby medical school in eastern Beirut, had come under intense shelling. The Army returned the fire, the broadcast said, adding that one Lebanese soldier had been killed and 13 wounded in earlier fighting.

In Zahle, the clergy of the Greek Orthodox community, which forms most of the city's 160,000 population, appealed to the Syrian Army, let Lebanese government and other parties to spare the town and its residents from the "mad and indiscriminate shelling." Telephone lines to Zahle were cut and for the second straight night it had no electricity.

Phalangist sources said the city was isolated from the rest of Lebanon. A ring of Syrian armor thrown around its outskirts and surrounding hills formed a blockade preventing delivery of food or medical supplies, they said.

Beirut radio said the Zahle-based Red Cross signaled its Beirut headquarters and the International Red Cross for medical equipment and blood.

Phalangist radio said tonight that 30 Zahle families were trapped in a bomb shelter under debris of an office building that collapsed when it was hit by Syrian artillery.

Today's renewed violence comes on the heels of official hopes for a defusion of tension with the Syrians. Reported plans of alternative security measures set by Lebanese and Syrian political and military leaders have met with skepticism, however.

A key element of policy for the weakened Lebanese government is to send its troops to southern Lebanon in order to reestablish central authority in a region now under control of Palestinian guerrillas, U..n. peacekeeping units and Israeli-backed Lebanese Christians.

Israel has been stepping up raids into southern Lebanon recently, reportedly at the behest of northern Israeli settlers who have demanded better protection from cross-border guerrilla raids.