Israeli forces, taking advantage of alleged cease-fire violations by Palestinian guerrillas, today tightened their noose around the predominantly Moslem western sector of the capital, where about 5,000 guerrillas and 1,500 troops of the Arab peace-keeping force, mostly Syrian-commanded Palestinians, are trapped.

Fighting centered around the science building of Lebanese University at the foot of the hills overlooking Beirut International Airport and near a main Palestinian guerrilla stronghold. There were conflicting reports throughout the day regarding which forces were fighting.

Israeli officers claimed that Bashir Gemayel's Lebanese Forces, acting increasingly in conjunction with Israeli forces, had shelled and taken over the six-story building. But the Christian Voice of Lebanon denied Gemayel's militias were involved.

Still, reliable eyewitnesses reported that Lebanese Forces commandos had captured the building.

The Palestine Liberation Organization news agency WAFA said the Israelis were attacking the campus and denied reports that it had fallen.

The creeping Israeli military grip on the high ground around the city came amid Lebanese efforts to get the newly formed National Salvation Council in operation and an agreement forged among the multitude of political factions for deploying the Lebanese Army in West Beirut.

Marwan Hamadeh, minister of tourism and a key figure in the negotiations, said a "package deal" was under intense debate; various sources reported it involved the future roles of the council and the Lebanese Army and a new status for the Palestinian guerrillas in the city.

Gemayel, leader of the Christian Lebanese forces, said after a meeting with President Elias Sarkis and his third encounter in 24 hours with U.S. special envoy Philip C. Habib that they also were discussing ways of "saving Beirut to avoid a repetition of Sidon and Tyre."

He was referring to the heavy civilian casualties and damage in those southern cities as a result of Israeli bombardments and fighting between Israeli forces and Palestinian guerrillas at the start of Israel's invasion 11 days ago.

Most here seemed to agree that the talks had reached a critical juncture, with a sharp deterioration in the situation at stake. But by nightfall no agreement was reported, and the Druze leader, Walid Jumblatt, who also heads the leftist National Movement, was still stubbornly refusing to participate.

Throughout the day, Habib met with Lebanese political leaders at the U.S. Embassy residence near the presidential palace at suburban Baabda. He was reported to be seeking to convince them of the urgency for the council to fill the political vacuum.

Under Sarkis, the council comprises leaders from the most important political factions, with three Christians and three Moslems on it.

A general feeling here today was that time was running out on getting the council off the ground and the Lebanese Army into the streets of West Beirut to maintain order and to forestall the entry of Israeli forces anxious to hunt down the Palestinian leadership.

"Had the Lebanese Army come a week ago it would have been better," remarked Saeb Salam, 77, a former prime minister and a key political broker in the negotiations. "Two days ago, it would still have been good, but now people only see weakness and vacillation."

One government minister said today that doubts were begining to grow in some political circles about the will or capacity of the Lebanese Army to defend West Beirut because of its failure so far to fight the Israeli invaders on any front.

"People are asking, 'If we get the Lebanese Army in, will it defend us or just let in the Israelis behind it?' " he remarked.

There were signs of a softening attitude by leaders of the Palestine Liberation Organization toward demands from various quarters that they accept a new status for their presence in West Beirut as the price for averting a showdown with the Israeli forces.

Hani al Hassan, a top political adviser to PLO leader Yasser Arafat, told Western reporters, "If America makes a step toward us, everything can be discussed. I mean the military aspect."

He was referring to reports circulating here that the PLO is now resigned to the partial, and possibly even total, disarming of its guerrillas and their confinement to camps if they stay on in West Beirut.

In return for this sharp reduction in their status to a primarily political movement, the PLO hopes to get the United States to recognize it, Hassan indicated.

Today, Prime Minister Shafik Wazzan held long talks with the PLO leader as well as Naif Hawatmeh, head of the independent Marxist Democratic Front, regarding the new status envisaged for the guerrillas.

Meanwhile, following the reports that the Lebanese University science building had fallen, the state-run Beirut radio commented, "There are fears now that Israeli forces will advance westward from the campus to take over the airport and storm into the refugee camps of Borj al Borajneh."

But even with the fall of the campus, the airport would hardly be safe for Israeli aircraft to land. Palestinians and their Lebanese allies are still within gun range to the south and east.

Israeli forces continued their steady spread along ground overlooking the capital and north through East Beirut up the coast, with Israeli jeeps spotted in and around the Christian port of Jounieh, 15 miles from here.

The Israelis seem to be using the Christian-held eastern sector not only to strengthen their military position but also for rest there and in the many coastal resorts just to the north.

To the east of the capital, Israeli and Syrian forces were almost within view of each other on the vital Beirut-to-Damascus highway. The Syrians have brought in tank and troop reinforcements to Aley, 10 miles east of here, and their advance checkpoint is only a few hundred yards from an Israeli one on the highway at Jamhour, according to local press reports.

Northeast of Beirut, Israeli forces, acting oblivious of the cease-fire, are also spreading out in the mountains behind the Christian enclave where the Syrian Army and pro-Syrian groups have positions.

Lebanese Forces officers said the Israelis had almost reached Aintoura, but analysts here doubted this, as the Israelis would have had to pass through Dhour Choueir, where the Syrian Army has a regional headquarters. Neither Syria nor Israel reported any fighting in that area today.