eavy fighting between Moslem and Christian militiamen spread today through the mountains southeast of Beirut, threatening to upset the relative peace the capital area has been enjoying since the arrival of the multinational peace-keeping force late last month.

Despite pledges from both the Lebanese and Israeli governments to step in and halt the escalating violence, neither had succeeded by nightfall in bringing it to an end.

[The Associated Press quoted Lebanese Information Minister Roger Shikhani as saying the fighting was finally halted by Israeli forces late in the evening. He told AP that Lebanese Army units would move into the area Thursday.]

Steady shelling by Christian militiamen of Moslem Druze villages continued throughout the day, and at one point late this afternoon two Israeli armored personnel carriers loaded with troops found themselves coming under the fire of their Lebanese Christian allies.

The fighting, which began on a minor scale a week ago, appeared to be shaping up as a serious challenge to the four-week-old government of President Amin Gemayel, whose control over his own party's militia -- held largely responsible for the flare-up -- is thought to be tenuous.

Lebanese Army troops apparently ignored the fighting and instead resumed their sweeps through the southern suburbs of West Beirut today for weapons and illegal aliens. The searches began Oct. 5 in the largely Moslem western part of the city but, despite government promises, they so far have not taken place in Christian East Beirut.

The Unified Command of the Lebanese Forces, a grouping of Christian militias nominally under the command of Gemayel, today notified the government that it would refuse to consider turning its weapons over to the Lebanese Army, the leftist daily Al Safir reported, according to Agence France-Presse.

Late this afternoon, a number of Israeli tanks and armored personnel carriers moved into the fighting zone in the mountainous area known as the Chouf, but shelling from Christian militiamen near the coastal town of Damur continued.

The Chouf is the stronghold of the Druze, a Moslem secret sect, but many of its mountain-crest villages also have Christians living in them.

Since the Israeli Army arrived in the Chouf in mid-June, it has been helping its longtime allies, the Christian Lebanese Forces once commanded by slain president-elect Bashir Gemayel, Amin's younger brother, to expand its presence and control over the area.

Resistance to the Christian militia push into the Chouf is being led by the Progressive Socialist Party whose chief, Walid Jumblatt, is currently on a visit to France. The Druze militia has been seriously weakened by the departure of the Syrian Army from West Beirut and the Chouf, since it had provided arms and extra muscle.

Most of the Christian militamen involved in the shelling are from the Damur Brigade, which was widely reported involved in the massacre of civilians inside two Palestinian refugee camps Sept. 16-18.

The Christians of Damur were forced out of the seaside town during Lebanon's 1975-76 civil war by Palestinian guerrillas aided by Jumblatt's Druze militia. They have now retaken the war-ravaged town and appear intent upon settling old scores both with the Palestinians and the Druze.

It is far from clear to most observers here whether the Damur Brigade is really under the control of the Lebanese Forces general staff in East Beirut or acting on its own in the present fighting.

At least five Druze villages about 15 miles southeast of Beirut were under attack by long- range rocket and artillery fire from the Christian militia's Maschref barracks just outside Damur. The fighting began flaring up a week ago and has slowly escalated ever since.

The most heavily hit was the mountaintop village of Bahwarta, where columns of heavy smoke could be seen rising this morning as shell after shell smashed into it. Casualties were not immediately known.

A short while later, rockets began falling on Abbey, located on another mountain crest across a valley from Bahwarta. Automatic rifle fire crackled intermittently.

The streets of Abbey were deserted when this reporter visited it this morning and most residents appeared to have evacuated the village or else were underground in shelters. Nonetheless, at least one car raced away with several wounded persons in it after one volley of rockets fell.

Watching the scene were two U.N. observers monitoring the situation. One Druze official pleaded with the two to do something to end the shelling, but they said there was nothing they could do other than report the shelling back to U.N. headquarters in Beirut.

Their response seemed to summarize the plight of the multinational peace-keeping force, consisting of 3,950 American, French and Italian troops, which is spread all across Beirut but has no mandate to intervene if fighting breaks out between Lebanese groups. The 50 U.N. observers are separate from the multinational force and operate outside the capital. As their title indicates, their function is simply to observe events and report to the secretary general of the United Nations.

This afternoon, Christian militia shelling was extended to Aber Shoumoun, to the north of Abbey, just as two Israeli armored personnel carriers showed up there apparently to try to restore the peace. Several shells fell within 50 yards of them as they raced for cover.

At nightfall, three Israeli tanks and one other armored personnel carrier were seen moving into the area but the shelling was still continuing.

As a result of the fighting, the supply of electricity to the capital was reduced to eight hours following the destruction of a piece of a cable line running through the area.