Beirut — As American Marines began a long-awaited withdrawal from Lebanon Tuesday, Israel again appeared to escalate its involvement in this divided country. While the Marines packed up, Israeli troops advanced northward from their southern Lebanon enclave to set up patrols near Damour, just 12 miles from Beirut. This was considered the most significant movement by the Israelis since they withdrew from that sector last September.
On the Lebanese political front, there was a flurry of activity as yet another formula was proposed to end the deadlock, this time apparently presented by Syria. But it failed to silence the thunder of artillery in the Shouf hills that overlook the Marine base at Beirut airport. Machine-gun, rocket, and mortar exchanges flared along the ''green line'' that divides Christian east Beirut from the Muslim west.
The fighting, together with the withdrawal of the Marines to the comparative safety of the Sixth Fleet after their 17-month stay, underscored the defeat of a US policy that had failed to:
* Secure an agreement for the pullout of 70,000 Syrian, Israeli, and Palestinian forces.
* Uphold Lebanese authority and sovereignty. The area under government control has shrunk from the capital and environs to only east Beirut.
* Rebuild the Lebanese Army, which fell apart faster this time than when it collapsed during the 1975-76 civil war.
* Establish a dialogue of reconciliation among the complex network of factions. The Muslims and Druzes are now more at odds with the Christians than ever.
Indeed, Lebanon is in a far more precarious state than when the US rushed in with political and military support after the Israeli invasion in June 1982.
A Marine spokesman, Maj. Dennis Brooks, admitted that ''there's a little frustration as (the Marines) feel our mission was not completed. But at least we kept the cap on the situation for 17 months to give the politicians a chance to talk.''
In private, many expressed bitterness about the pullback. They felt that 260 Marine lives were lost with nothing to show for it. The mood at the base Tuesday was somber - almost anticlimatic.
Capt. Kevin Baesler was in the first group to leave. Like many of his colleagues, he felt the Marine mission was no longer feasible: ''If these people ever work out their differences in the next year, I'll be really surprised. It just seems everyone here is very polarized.''
The withdrawal, which the Marines repeatedly stress is only a relocation and not an abandonment of Lebanon, is expected to take at least a week, Major Brooks said. Indeed, there was no sense of urgency or mass movement, except for the constant drone of low-flying Sea Stallion and Sea Knight helicopters shuttling between ship and shore. An armada of more than 20 US ships lies off the coast to provide living quarters and protection for the 1,300-man contingent.
The major question in Beirut now is who will take control of the Marine complex of underground bunkers near Beirut airport, still closed because of the fighting.
In what appeared to be an attempt to avoid a confrontation for control of the terminal and runways, defectors from the Lebanese Army's 6th Brigade moved in Tuesday morning. The Druze and Shiite factions had agreed to deploy Army and gendarmerie units sympathetic to the Muslims instead of militiamen at all public facilities in west Beirut.
Israel, meanwhile, bombarded positions in Lebanon for the second time in 48 hours. An Israeli spokesman said the targets were four buildings used as ''terrorist headquarters and bases'' along the Beirut-Damascus Highway.
The raid came just hours after Shiite leader Nabih Berri announced that the Lebanese opposition militias had met with Palestinian guerrillas in Damascus, where they agreed that no armed Palestinians would be allowed to return to Beirut. The Israeli attacks on Syrian-held positions led Druze forces to open up with antiaircraft guns.
Israeli troops also closed in on the ground, moving up troops from behind the southern Awali River for ''wide-ranging patrols'' near Damour - the front line for the opposition militias since the Druzes took control of the coastal road last week.
Beirut radio stations interpreted the advance as a warning to the Druzes and their allies not to allow a renewed Palestinian presence, and not to advance any farther toward Israeli-occupied southern Lebanon.
(Israeli Prime Minister Yitzhak Shamir said Tuesday a locally recruited Lebanese force might be able to replace Israeli troops occupying southern Lebanon and secure Israel's northern border, Reuters reported.)
Meanwhile, the latest peace plan for Lebanon was reportedly presented to Lebanese President Amin Gemayel late Monday.
* Abrogation of the controversial May 17 troop withdrawal accord between Israel and Lebanon.
* Agreement that Syrian and Israeli troop withdrawal from Lebanon must not be treated on the same basis. The issue of Syrian troops would be taken to the 21 -nation Arab League for debate.
* Resumption of the reconciliation talks among Lebanese factions, which would introduce reforms to even the balance of power between majority Muslims and minority Christians.
Although there was no official comment on the plan, diplomatic sources said Mr. Gemayel was not pleased.