With its infantry moving cautiously from block to block behind protective columns of tanks and armored personnel carriers, Israel today occupied Moslem West Beirut.

Fighting for the first time in the heart of an Arab capital city, the Israeli units fanned through West Beirut's shuttered commercial heartland and its densely populated residential districts, fighting sporadic engagements in the streets with disorganized bands of lightly armed leftist militiamen.

The Lebanese government protested Israel's takeover of the city, which had resisted siege throughout the summer when it was defended by about 11,500 now-evacuated guerrillas of the Palestine Liberation Organization. Lebanese officials claimed that the invasion violated explicit guarantees by the United States that it would not allow Israel to enter the city once the PLO had withdrawn.

The U.S. guarantees that it would block an Israeli invasion, West Beirut Moslem leaders said, were contained in unpublished appendices to the PLO withdrawal agreement negotiated by U.S. special envoy Philip C. Habib.

"I appeal to the United States and ask how far it will abide by its pledges and guarantees," Prime Minister Shafiq Wazzan said today in a radio address after he had sent urgent requests to Washington to pressure Israel to withdraw immediately. His requests were made directly to U.S. envoy Morris Draper, Habib's former deputy here, who returned to Lebanon yesterday to resume negotiations for the withdrawal of all remaining foreign forces in Lebanon. In addition to the Israelis, these include Syrian and PLO units camped in the eastern Bekaa Valley and northern Lebanon.

There were no immediate reports of the number of casualties today. Yesterday, in the first day of fighting, Israel reported two of its soldiers were killed and 42 wounded. The Nasserist Morabitoun, the dominant Moslem militia, said today that five of its men were killed and seven wounded in fighting the Israeli advance this morning.

Ambulances wailed through the mostly deserted streets during the day. The city sporadically resounded with the rattle of machine-gun fire and the loud snap of tank cannons crashing through the terrified Moslem sector of half a million people, many sent fleeing in panic from their neighborhoods.

With Israeli tanks blasting away at suspected sniper positions in office buildings within West Beirut's center along Hamra Street, with the Lebanese Central Bank afire from a random Israeli shell, and with Israeli armored forces crisscrossing the city's residential areas to engage leftist militiamen in a series of hit-and-run battles, Wazzan said that not only U.S. honor was at stake in Lebanon, but also the whole credibility of the Reagan administration in the Arab world where it has sought to curry favor through its Middle East initiative announced last week.

"I make a direct appeal to U.S. officials, to President Reagan, Secretary of State George P. Shultz and Habib, in particular, and ask them how they want the Arab world to look at their peace initiative and promises after this," Wazzan said. "The responsibility of the United States is great. We are waiting, the whole world is waiting, for American action."

Israel, whose June invasion of Lebanon was considered to have aided the election of Lebanese president-elect Bashir Gemayel, who was assassinated Tuesday, had counted greatly on Gemayel's forceful presidency to control divided Lebanon.

Tonight, Gemayel's Phalange Party moved to fill the vacuum created by its leader's death, according to well-informed sources, by nominating Bashir's elder brother, Amin, 40, as its candidate for the parliamentary presidential election expected to be held before Sept. 23.

Wazzan today rejected Israel's explanation that it had moved into West Beirut to thwart any regrouping of Palestinian and leftist forces as "irrelevant" and "false," saying that his government's deployment of national policemen and Lebanese soldiers in West Beirut in the wake of the PLO withdrawal Sept. 1 had been gradually restoring order and government authority in war-battered West Beirut.

Moslem leaders point out that both before and after Gemayel was killed in a bomb explosion in an office of his Phalange Party in East Beirut, calm had been returning to West Beirut. Leftist Moslem militiamen there had been gradually turning over their militiary positions to the police and the Army under a security plan negotiated by Wazzan with the local militia leaders.

The Lebanese government also sought help in getting the Israelis to withdraw from Saudi Arabian King Fahd, whose influence with Washington is considerable, and from French Foreign Minister Claude Cheysson, who met with government leaders here today after flying from France to pay condolences to Gemayel's family.

Fahd has promised Lebanese leaders that he would do his best to end the Israeli occupation of their capital, according to an official Saudi news agency dispatch reported by Reuter. The king was said to describe the occupation as inhuman and unjustified.

Wazzan is understood to have asked Cheysson to send back the Foreign Legionnaires who departed Monday night. His appeal echoed that made by PLO Chairman Yasser Arafat in Rome today in which he called for the return of the multinational force to Lebanon.

Lebanese Army troops that had been deployed only last week between the Israeli lines and the city's undefended southern suburbs to act, in accordance with the Habib plan, as a security cordon for the capital, simply moved aside without a word of protest or a shot fired when the Israelis began to move their tanks, armored personnel carriers and troop-carrying half-tracks into West Beirut.

Apparently having ascertained yesterday that the resistance from the city's assortment of irregular leftist militia groups was spotty at best, Israel took control of the port of Beirut and yesterday at noon landed two brigades from ships for an attack westward across the so-called Green Line of battered buildings that has divided the Lebanese capital since the 1975-76 civil war.

After a lull in the fighting last night, the Israeli Army completed its drive for control of the Moslem sector today. Armored columns moved quickly through the once-fashionable seaside hotel district, gutted during the civil war, and then split, with one force racing down the seafront esplanade on which the U.S. and British embassies sit while a second column moved up toward Hamra Street, firing cannons at every intersection either at suspected militia sniper posts or just to scatter potential opponents.

The French Embassy had two phosphorous shells land in its spacious grounds. The Central Bank was hit as were at least four cars and three office buildings along Hamra Street.

Groups of youths, in civilian clothing and armed only with Kalashnikov assault rifles and antitank, rocket-propelled grenades, tried, with little success, to stall the Israeli drive.

Even without big guns, the militiamen had a few successes. Two Israeli tanks were destroyed early this morning near the burned-out hulk of the city's former Holiday Inn. At least one other Israeli tank was destroyed near the city's southern sports complex that had served once as a PLO military academy.

Israeli tank columns along the coast joined up early this morning with other forces that had moved through the town from the south, after first surrounding the already battered Palestinian refugee camps of Burj al Barajinah, Shatila, and Sabra.

Having linked up on the coast this morning, the Israeli columns spent the rest of the day crisscrossing through the city at will, attacking suspected militia headquarters and neighborhoods where they were based, setting up roadblocks to check for identity cards, and arresting suspects.

The Israeli Army also chased the Lebanese Army from some of their recently reoccupied barracks in West Beirut; at the seaside barracks of Bains Militaire, where even under the reign of the PLO the Lebanese Army had been allowed to remain, the Israelis dug in half a dozen tanks, sent their men into the barracks and sent the Lebanese away in trucks and jeeps.

Dense clouds of smoke, black and gray, rose every now and then over the city from the refugee camps to the south, from the east-west boulevard of Corniche Mazraa where the fighting was heaviest, and from near the Green Line where the odd tank or passenger car had been set aflame. By nightfall the fighting had died out in the city center, but gunshots and occasional cannon booms could be heard from the vicinity of Gamal Abdel Nasser Mosque on the Corniche Mazraa, the headquarters of the Morabitoun.