The Israeli Army invaded major sections of West Beirut today in a six-pronged thrust that started at dawn, just hours after the government officially announced the assassination of President-elect Bashir Gemayel.

The Israeli force included tanks, armored personnel carriers and infantrymen. It met with little resistance from Moslem leftists who had taken over Palestinian positions following the guerrillas' withdrawal last month or from Lebanese government forces.

By evening the Israelis had penetrated 2 1/2 miles deep into West Beirut. They occupied not only areas that had served as centers for the Palestine Liberation Organization before its evacuation last month but also sections that had been outside the guerrillas' control.

Observers suggested last night that the Israelis were intent on occupying all of the capital.

During the 10-week siege of Beirut, Israeli troops had never ventured into these areas. They had been heavily defended by the PLO until U.S. special envoy Philip C. Habib negotiated the PLO's withdrawal Aug. 12.

West Beirut Moslem leaders gathered in an emergency session late today at the home of former prime minister Saeb Salam and decided to appeal urgently to President Reagan and King Fahd of Saudi Arabia to "curb the Israeli invasion of our capital."

Israel announced that its actions were taken to prevent anarchy after Gemayel's assassination, Washington Post correspondent Edward Walsh reported from Jerusalem. He said Israeli radio reported Jerusalem had assured the United States that it would end its military moves in 24 hours. Details, Page A34.

Prime Minister Shafiq Wazzan protested to U.S. charge d'affaires John Pugh that the Israeli assault was a direct violation of the cease-fire established by Habib. He also charged that the attack violated the terms of the U.S. agreement that provided for both the PLO withdrawal from Beirut and for an Israeli easing of its grip around the city.

Israeli claims that their move had been prompted only by the uncertainties resulting from the death of Gemayel, a man they had backed and armed since the height of the 1975-76 Lebanese civil war, were challenged by other Moslem leaders.

They claimed Israel had planned the attack all along, pointing as evidence to the Sept. 3 Israeli violation of the cease-fire and the Habib accords by moving north of the airport into a residential and foreign embassy neighborhood called Bir Hasan, previously occupied by the PLO.

Moslem leaders charged this move violated the agreement that Israel would not take advantage of the vacuum created by the PLO departure. They also noted that it allowed the Israelis to clear mines in the areas, thus opening the highways that their tanks and armored personnel carriers used today in their move northward.

The Israeli assault began with mock bombing attacks by jets and then a three-pronged attack of tanks, personnel carriers and infantrymen up three main highways south of the city in an area of refugee camps and residential areas that had been a PLO bastion.

Three other thrusts came later in the day out of East Beirut across the Green Line that has divided East and West Beirut since the civil war: one by the port, one at the commercial district just to the south, and the third at the National Museum crossing.

The move by the Israelis from positions just north of the Beirut International Airport, which they have occupied since the begining of August, moved past a line of recently deployed Lebanese Army soldiers. According to U.N. observers, the soldiers did not resist the Israeli advance and seemed to fade away as the Israeli columns moved north.

The Israelis were met with only sporadic resistance from rapidly mobilized local Moslem and leftist militias. The militias seemed to be armed only with small arms and rocket-propelled grenades though they knocked out at least two Israeli tanks in the early morning.

Israel's military command said two of its soldiers were killed and 42 wounded in the assault.

The three major highways used in the southern attack parallel the coast, one being the coastal road through the neighborhood of Janah, the other the Avenue Camille Chamoun that flanks the Sabra and Shatila Palestinian refugee camps, and the third, the airport road extension of Avenue Jamal, which passes by the Shatila camp's eastern flank.

The westernmost Israeli column on the coastal road moved along the four-lane Avenue Ramlet el Baidah, site of the still-incomplete new U.S. Embassy building. It reportedly had reached the intersection with the major west-east boulevard, Corniche Mazraa, that divides the southern part of West Beirut from the more populated residential district to the north.

Fourteen Israeli gunboats had taken up station just offshore from West Beirut and had lobbed cannon shells into the Ramlet el Baidah Avenue north of the tank formation to clear it. Scattered cannon fire rained also into the Raouche district north of Corniche Mazraa, which had been badly bombed and shelled by the Israelis during their summer-long siege.

The Lebanese state radio announced that the Israelis had also moved into the Palestinian shantytown of Sabra, one of the PLO's former base areas.

By nightfall, some of the Israeli advance columns were reported by police officials as having gone as deep as 2 1/2 miles into the city.

The northern Israeli move pushed into the warren of shell-pocked buildings of the former PLO neighborhood of Fakhani, just north of the two camps.

Another Israeli force moved into West Beirut's old Jewish quarter of Wadi Abu Jamil in the old commercial district south of the port tonight. Lebanese police said it appeared to be moving toward the Murr Tower, an uncompleted 40-story skyscraper that was abandoned last week by leftist militiamen.

In the northernmost move, an Israeli armored column, made up of 10 U.S.-made M60 tanks and nine armored personnel carriers, advanced through the port's western gate four blocks into the zone of abandoned and rubble-strewn buildings that form the Green Line. The column earlier had been moved into the port area that was abandoned only two days before by the last French contingent of the multinational force that had supervised the PLO's withdrawal.

The area was being defended by the left-wing Morabitoun militia, that had taken over positions held by the Syrian-dominated Palestine Liberation Army prior to its evacuation.

Israeli tank shells crashed sporadically around the burned-out Holiday Inn and the gutted waterfront Hotel St. Georges.

The attacks caused panic among West Beirut residents just as they were reeling from the news that Gemayel, who many of them originally opposed but had been coming around to accepting, had been killed.

Meanwhile, the Lebanese government announced today that the bomb that blew up the local headquarters of Gemayel's Phalange Party in East Beirut's Ashrafiyea district yesterday had killed 26 party aides of the president-elect and wounded 60 others.

The bomb, estimated by Phalange Party munitions experts as having been made up of 440 pounds of TNT, blew out the three-story Phalange Party building 20 minutes after Gemayel had arrived there.

The government said Gemayel's body had been badly mangled in the explosion.

Gemayel, who had many enemies, among fellow Christians whom he had warred against in his rise to power and among the Moslems he fought during the civil war, was elected against strong Moslem opposition Aug. 23. He was to have been inaugurated for a six-year term Sept. 23.

His funeral was conducted this afternoon at Bikfaya, the town where he was born. As Lebanese political leaders, Christians and Moslems alike, gathered there, the sounds of the Israeli attacks could be heard in the coastal plain.