Fighting between Shiite Moslem Amal militiamen and Palestinian guerrillas on the southern edges of Beirut intensified dramatically overnight and Shiite military commanders called on their forces in the Bekaa Valley and Hermel Mountains to join the growing confrontation.

Battles raged at daybreak today and Amal, determined to frustrate any attempt by Palestinian fighters to move outside the refugee camps where they are based, put its Syrian-supplied Soviet T54 tanks into action to repel advances outside the sprawling shantytowns.

Despite widespread condemnation by Lebanese officials, the camp war, sparked 12 days ago by an influx of Palestinian guerrillas and arms into west Beirut, threatened to spill over into other parts of the city.

Amal is trying to prevent Palestinians, who have been filtering back into Beirut after being expelled by Israel in 1982, from regaining their military foothold in Moslem-controlled west Beirut.

The main airport road was closed to traffic this afternoon as shells and mortars thudded around the Sabra, Shatila and Burj al Barajinah refugee camps, driving about 500 families from their huts. The casualty toll from both sides was estimated at 35 dead and more than 100 wounded during the 12 days of fighting. A year ago, five weeks of bitter fighting for control of the Palestinian camps led to 650 deaths and at least 2,000 injuries.

The Damascus-based Palestinian Salvation Front, an alliance of guerrilla groups, said Amal fighters had thrown a blockade around the camps, barring the supply of food and other essential materials, including medical aid.

Akel Hamiyeh, a senior Amal militia commander, appealed to "our people in the Bekaa and the tribes of the Hermel Mountains to start preparing themselves for a hard blow against the traitors," meaning the Palestinians. The escalation of the fighting attested to rumors of the infiltration of thousands of Palestinian guerrillas back to Beirut by sea through Moslem militia-run ports near the city.

Amal leader Nabih Berri, a Cabinet minister, has accused Lebanese President Amin Gemayel of making a deal with Salah Khalaf, a top aide of Palestine Liberation Organization chief Yasser Arafat, for the return of Palestinian fighters to Beirut. Gemayel reportedly met Khalaf, better known as Abu Iyad, during a tour of Arab nations two weeks ago.

Berri dispatched two senior Amal envoys to Damascus today to confer with Syrian officials on the crisis. Berri told a delegation of Arab journalists he had asked Algeria and Iran to mediate an end to the fighting between his militiamen and the Palestinians.

Despite differences among Palestinians, various guerrilla groups united last year to resist the threat by Amal and its local allies. Palestinian gunners entrenched in the Druze-controlled mountains joined the battles last year against Amal to relieve pressure on the besieged camps.

It was not clear whether Palestinians in the mountains had joined in the most recent round of fighting.

Residents in Beirut's Shiite suburbs said their areas were coming under shelling from all directions. Amal military sources reported that Palestinians were massing men and armor inside the camps in preparation for an assault against militia positions at the periphery.

A cease-fire was declared following an Amal-Palestinian meeting this afternoon, but it broke down within minutes of its announcement, Palestinian spokesmen said.