The final phase of the withdrawal of Palestinian and Syrian fighters from West Beirut began today with the first of a series of overland evacuations from the siege-smashed Moslem sector of the Lebanese capital to Syria.

To the now routine final salute of wild gunfire into the air, an estimated 1,300 members of the Syrian-controlled Palestine Liberation Army's Hittin Brigade drove out of the city today in a motley convoy of vehicles through the Galerie Semaan exit point that was manned by a detachment of Italian Bersaglieri soldiers sporting white helmets with drooping ostrich plumes.

Israeli complaints about the counting of the Palestinians delayed the convoy, which was already two days late getting started, for another half hour, but then it was under way. Hours later, after a triumphal entry into Syria, the convoy reached the Palestinian refugee camp outside Qatana, southwest of Damascus, where the fighters are to live.

Moving in a column of more than 200 troop transports, wooden-sided cattle trucks, buses, vans and jeeps, all sporting pictures of Palestine Liberation Organization Chairman Yasser Arafat and Syrian President Hafez Assad, the convoy left the city with Palestinian flags flying, guns blazing at the sky and the evacuees striking heroic poses with their assault rifles held high over their heads.

The men were part of the PLA brigade of some 3,500 men that Syria sent into Lebanon in 1976 as part of their army's Arab Deterrent Force of 30,000 troops mandated by the Arab League to end the Lebanese civil war.

Today's members of the Hittin Brigade, one of the Palestinian units that fought hardest against the Israeli army that pinned them into a punishing siege of the city, carried with them truckloads of bedding, cooking ware, tables, chairs, and even Japanese motorcycles strapped on top of a truck, as well as cartons of the U.S. cigarettes that will be in short supply in their new home in Syria.

The U.S.-mediated agreement for the evacuation of the PLO fighters that ended Israel's 10-week siege of Beirut stipulated that Israeli forces would pull back from the convoy route in the mountains east of Beirut to remain unseen by their opponents. But the column was barely under way this morning when it was halted by a jeepload of Israeli soldiers who demanded a more accurate count of the evacuees. Under the agreement the Lebanese Army, backed up by a multinational force, is supposed to check the number of PLO fighters leaving the city.

In a seeming violation of the evacuation plan negotiated by U.S. special envoy Philip C. Habib, the Israelis delayed the convoy for half an hour before Lt. Col. Brumer Tosetti, commander of the Italian forces, persuaded them to let the convoy proceed.

Once the convoy took off, it wended its way through the mountain villages that dot the winding road from Beirut to Damascus. Blue-and-white Israeli flags with the star of David had been hung along the route and the Syrians spat on the highway as they passed.

At one point Gen. Amir Drory, commander of Israeli forces in Lebanon, raced in and out of the slow- moving convoy in his command Land Rover, flashing V-for-Victory signs at the evacuees, who angrily looked away.

It was the second time Israel temporarily halted the withdrawal, which over a two-week period is to remove an estimated 7,100 PLO fighters and 5,000 Palestinian and Syrian regular soldiers of the PLA and the Syrian Army. Last Sunday Israeli gunboats blocked the departure of a ferry carrying PLO soldiers to Tunisia because they had put 21 vehicles aboard.

Israel let the ship proceed only after the U.S. government agreed to guarantee that the vehicles would be unloaded in Cyprus.

Today's brief delay was overshadowed by the fact that after six days of evacuating the fighters in relatively small numbers by sea, the overland evacuation route over which the bulk of them are scheduled to pass had finally been opened.

The first scheduled overland departure was postponed Wednesday after the PLO balked on the grounds that security had not been adequately guaranteed along the narrow road that passes near many positions held by the Israeli army or the militia of its Christian Phalange Party ally.

The success of today's overland exodus, coupled with the departure of another 675 PLO fighters from the port by ferry taking them to Tartus, Syria, brought to almost 6,500 the total evacuated in the first full week. The withdrawal is scheduled to end Sept. 3, but U.S. officials have said it might be completed ahead of schedule.

Sen. Charles Percy (R-Ill.), chairman of the Foreign Relations Committee, reiterated that view today during a seven-hour trip to Christian East Beirut from Cyprus, where he was visiting.

After touring the Beirut port area, which is guarded by 800 U.S. Marines, part of the 2,130-man international peace-keeping force here, Percy said his talks with U.S. and Lebanese officials left him confident "the evacuation will be completed more rapidly and with fewer difficulties than had been anticipated."

Before visiting the Marines, Percy met with Habib, Lebanese President Elias Sarkis and President-elect Bashir Gemayel.

Percy appeared clearly impressed by Gemayel, 34, the Christian militia leader whose election has sent waves of apprehension through the country's Moslem majority, which fought a civil war against Gemayel's forces in 1975-76.

Percy said he would tell his fellow congressmen and President Reagan of Gemayel's "political and humanitarian intentions and his desire to bring order, peace, and stability to Lebanon for the first time in many years."

In West Beirut, however, Moslem leaders have continued to threaten not to cooperate with Gemayel unless he pledges to seek to continue the Christian-Moslem consensus on which all previous governments have tried to base themselves. They are also demanding that Gemayel make it his priority to get Israel to withdraw from Lebanon.

Although the PLO is finally leaving Beirut, its leftist and Moslem Lebanese allies remain in their positions facing both the Israeli army and Gemayel's 20,000-man private militia.

Armed with new weaponry--tanks, artillery, antiaircraft batteries, mobile rocket launchers--that the PLO has turned over to them in apparent contravention of the evacuation agreement, the West Beirut militias are determined to prevent the next president from imposing his rule on their communities by force, either through the Lebanese Army, which the Moslems mistrust as a Christian-dominated force, or Gemayel's own loyal nationalist Christian Lebanese Forces.

The position taken by West Beirut's Moslem leaders has delayed deployment of the Lebanese Army alongside the French, Italian and U.S. peace-keeping forces along the line dividing the city.

With the leftist militias holding their positions near the main crossing points--the Galerie Semaan and the National Museum--the untested Lebanese Army that had to be rebuilt from scratch after its split during the civil war has balked at taking up positions across from such groups as the Nasserist Morabitoun that controls large areas in the city center, including the National Museum, where French paratroopers have taken up positions.

The expected deployment of the Lebanese Army inside West Beirut, as envisaged in the Habib plan to bring law and order to the anarchic city, has also failed to materialize so far because of Moslem opposition.

Negotiations yesterday, however, resulted in Moslem leaders agreeing that Lebanese security forces, the special police and gendarmerie, could enter the western sector. But Army units that are to back them up will still have to remain in their barracks, according to the agreement negotiated between the government of Prime Minister Shafiq Wazzan and the Islamic bloc that groups the nation's dominant Sunni and Shiite Moslems leaders and the Druze of Socialist Walid Jumblatt.