Israeli forces today took up positions in the shadow of the presidential palace at Baabda, on the heights overlooking the Lebanese capital, and with the Lebanese Christians completed their encirclement of remaining Palestinian guerrilla strongholds on the southern outskirts of the city.

The Israelis also immediately began moving an armored column northeast, apparently in an effort to clean out armed pro-Syrian groups based on the mountains overlooking Lebanon's Christian enclave.

Despite the Israeli movements, Beirut was calm today. Only a few rounds of artillery could be heard in the distance from Baabda in the morning.

The relative quiet followed heavy fighting Sunday as a cease-fire between the Palestine Liberation Organization and the Israelis broke down and the Israelis moved armor and troops into the Beirut area through the night.

After the Israelis had established their positions here, Defense Minister Ariel Sharon and Army Chief of Staff Raphael Eitan visited the area and spent the night.

Today, in an effort to quell rumors regarding the location and morale of the Palestinian leaders, PLO leader Yasser Arafat and several of his deputies toured troop positions, refugee camps and hospitals in West Beirut.

Arafat briefed his followers on the current situation and assured them that "the revolution will stand firm in its position."

Israel's Eitan was quoted by United Press International as saying Arafat had taken shelter in an unidentified foreign embassy in Beirut.

But the toll reportedly has been high for the Palestinians. Lebanese police reported today that 9,583 people have been killed and 16,608 wounded since the Israelis began their air raids 11 days ago. They put the number of dead in Beirut at 750. Israeli officials disputed the high toll, however, and it was unclear how the police reached their calculations since much of the hardest-hit areas are in southern Lebanon and are still under Israeli control.

Dozens of tanks and armored personnel carriers this morning moved in around the presidential grounds, which is located in an area controlled by the Christian-Maronite militia commanded by Bashir Gemayel, who in the past has cooperated with the Israelis. Today Gemayel's followers greeted the Israeli troops as liberators.

Col. Amos Neeman, 46, spokesman for the Israeli forces in Baabda, said they had arrived overnight after engaging in a "very heavy fight" with Syrian troops and Palestinian guerrillas four miles down the road at Bsaba.

Neeman denied that the Israelis wanted to take control of Beirut's international airport, the scene of bitter fighting in the past several days. But he later added that Israeli forces might move to improve their positions "a little" in the coming days. He also said, "We don't want any fighting in the city of Beirut."

Already by nightfall, the state-run Beirut radio reported Israeli tanks and armor had moved through the Christian-controlled section of Beirut and were taking the road to Aintoura in the mountains east of Beirut.

The apparent aim of the latest new Israeli military thrust into the mountains was to clean out Syrian and pro-Syrian factions holding positions behind the Christian enclave north of Beirut. This would not only expand the area under the control of Gemayel's militia but also would reduce still further the bargaining leverage of the Syrians in Lebanese politics.

One of the main goals of the Israeli invasion of Lebanon, now in its ninth day, has been to oust Syria, with its 30,000-man Arab peace-keeping force, from the country. Neeman said today that "the Syrians are now out of the picture" around Beirut except for some isolated units still holed up in the mountain slopes between Baabda and the coast.

"We are not going to play any role in changing the way of life in Beirut," he said. "That is their own problem. We just want to get rid of the Syrians."

Later Beirut radio reported 40 Israeli armored personnel carriers were spotted in one section above Christian East Beirut and that the Israelis were laying down lines of communication through parts of another sector.

Meanwhile, the Israeli forces have now completely surrounded the Palestinian guerrillas and their Lebanese allies fighting in a 10-square-mile area just south of the capital and also have gained control of the exit roads leading eastward to the vital Beirut-Damascus highway.

One PLO source described the situation following the arrival of Israeli forces at Baabda as "a new ball game," with the Palestinian and Israeli forces now "eyeball to eyeball and neither side blinking."

But he denied the PLO leaders had any intention at all of leaving West Beirut and declared the Israelis "will never get into this city."

The Palestinians have perhaps 5,000 guerrillas still in West Beirut and are intent on conveying the impression to outsiders that there may even be more here ready and anxious to fight the Israelis on their turf.

Arafat, during his tour of Palestinian strongholds, was reported to have told troops, "There is no force on Earth which can make us give up our weapons." Accompanying him was Abu Jihad, a Fatah Central Committee member, and other unnamed PLO officials.

Neeman blamed the high casualties reported by the Lebanese partly on the Palestinian practice of setting up their military positions in the main streets of towns and in the homes of civilians. But he also admitted Israeli forces had made ample use of artillery to soften up guerrilla positions and encourage them to flee, adding "There could be some mistakes but it was not our intention."

One Israeli soldier said the Israelis had literally blown away the houses in which the Palestinians holed up, killing the residents as well as the guerrillas inside.

Despite professions of strict neutrality in the Israeli invasion by Gemayel's spokesman, Neeman said officers of the Christian militia had aided the Israeli forces as guides up the road from the coast and said that the Christians had received them like a "liberation army," showering them with flowers and candy and offering them cakes and drinks.

"Since we entered the Christian area not a single shot has been fired at us," he said.

The Christian militia's military police and other officers of Gemayel's Lebanese forces could be seen working hand in hand with the Israeli troops around Baabda this morning, and one reporter was shown two Syrian tanks that the Lebanese claimed to have destroyed when the vehicles tried to retreat yesterday from the fighting below here.

The scene at Baabda and nearby Hadath, where eight Israeli armored personnel carriers and one tank were parked just off the side of the road, was festive.

Christian Lebanese streamed by in cars waving to Israeli soldiers while smiling young girls walked by flirting with them. Some were offering them cakes while others sought to exchange money or souvenirs.

"They are our only hope," said Brenda Khouri, 18, who stood with her father on the road just below the government palace with tears in her eyes watching an Israeli armored personnel carrier roar by her home.

"They are welcome," agreed her father smiling at the scene.

The Israeli soldiers, many of them of North African origins and speaking Arabic, seemed somewhat confused but delighted at the friendly reception they were getting after fighting through hostile territory for days since they landed north of Damour early last week. Some of the soldiers were asking about the latest results of the World Cup soccer championship in Spain, the war in the Falklands, and in one case, how to make a call to Israel to assure his wife he was safe.

One of the soldiers, who refused to give his name, remarked somewhat defensively, "We are not here to conquer anything. We are just here to defend our people."

Asked where they were going next, he replied, "We want to go home."