Israel warned the Lebanese government today that the Israeli Army would advance further into West Beirut unless leftist militiamen facing its troops in the city's southern outskirts withdraw.

Israeli Defense Minister Ariel Sharon issued the warning in comments to reporters as he toured new Israeli forward positions in the southern Beirut neighborhood of Bir Hasan. U.S. officials passed the same message to Lebanese Prime Minister Shafiq Wazzan, official Lebanese sources said.

The Israeli military command demanded the immediate return of eight Israeli soldiers who were captured over the weekend at an observation post near Syrian lines in eastern Lebanon, Washington Post correspondent Edward Walsh reported from Jerusalem. Israel termed the capture "a most serious violation of the cease-fire."

Israeli troops advanced into Bir Hasan on Friday in apparent violation of the "cease-fire in place" that took effect Aug. 12 when the Israeli government accepted a plan negotiated by U.S. special envoy Philip C. Habib that provided for the now-completed evacuation of Palestine Liberation Organization guerrillas from Beirut.

Bir Hasan, a neighborhood of Arab embassies, modern apartments and two U.N. office buildings, was the PLO's southern line of defense throughout the summer-long siege of Beirut. The Israelis said that they had moved into the area only to cover mine-clearing operations, but they did not withdraw after the operations were completed and have taken up positions in several buildings there including the two U.N. ones. The Israelis also occupied the embassies of Hungary and South Yemen which diplomats fled during the Israeli siege.

Today, Sharon inspected his troops in the U.N. buildings and told reporters that, if leftist militiamen who have moved into the rubble of buildings in the Jnah district just north of Bir Hasan did not withdraw, his forces would move farther north to force them out of the area. The zone guards the western flank of the Palestinian refugee camps of Sabra and Shatila, which once were major PLO bases.

Sharon said Israel would not withdraw its forces from around West Beirut until it was convinced that Beirut would not become again a "center of terrorism." He claimed that not only were there about 1,000 armed Lebanese "terrorists" still in the capital but also that the PLO had left behind 2,000 of its own guerrillas in Beirut despite the evacuation of 14,500 of its main troops and their Syrian allies in the operation completed last week.

Lebanese officials viewed Sharon's warning and the continued Israeli Army presence in Bir Hasan as part of a campaign to pressure the government to collect heavy weapons given by the departing PLO to Lebanese leftist and Moslem militias.

Wazzan held another round of meetings with West Beirut's Moslem leaders to discuss the Israeli demands. Officials close to the prime minister said he was concerned that Sharon might order a push into West Beirut unless the militias could be convinced to give up their heavy weapons and withdraw from Jnah.

Sporadic shooting incidents have occurred during the past few days between the Israelis in the southern suburbs and the leftist militias holding positions nearby.

Meanwhile, a spokesman for the International Red Cross here said that it so far had been unable to ascertain who was responsible for the capture Saturday night of eight Israeli soldiers from a forward observation post near the town of Bhamdun 15 miles east of Beirut. The Israelis asked the Red Cross to inquire about the men, who Israel says were taken alive and led off.

Israeli officials announced yesterday that the men were missing and said they clearly had been marched by their captors into nearby Syrian lines. An Israeli officer in Bhamdun said today the men had been "hijacked" and that "we are pretty sure the Syrians know where they are."

The radio for the Morabitoun militia announced that the soldiers had been captured by "joint forces," a term referring to the alliance of PLO and leftist Lebanese militia guerrillas.

Correspondent Walsh added from Jerusalem:

In condemning the capture, the Israeli command said, "A cease-fire is supposed to be in effect, not a war, and the capture of the eight men was an act of kidnaping. Israel knows the men were captured alive and well and expects them to be returned in the same condition."

The incident was not only a potential source of new tension between Israeli and Syrian forces in Lebanon but also an acute embarrassment to the Israeli Army, which was lauded by political leaders over the weekend for its performance during the war in Lebanon.

The independent newspaper Haaretz said the capture of an entire Israeli outpost in daylight without a fight was "one of the worst failures in ongoing security in Israeli Defense Forces' history."

It remained unclear today whether Syrian troops or Palestinian forces had captured the soldiers. In either case, officials said, Israel would hold Syria responsible for the men.