Beirut — The pace of both United States and Saudi Arabian efforts to contain Lebanon's ''war of the mountains'' has quickened as Syrian-backed Druze militia steamroll rapidly over Christian Phalange gunmen outside Beirut.
The speed of the Druze thrust has made peace negotiations more difficult, giving Muslim leftists and Syria a stronger case for their demands, according to Western diplomats.
Druze forces of the Progressive Socialist Party have captured a series of towns and villages in the Alery and Shouf mountain regions, including the strategic town of Beit ed Dine, the site of the presidential summer resort.
The campaign now appears close to reaching the Mediterranean coast south of Beirut, thus partially surrounding the capital and completely cutting off south Lebanon.
Druze forces also launched a major attack Saturday night against the crucial town of Souk al Gharb, the only town in the Shouf held by the Lebanese Army. Western military officials said it was the heaviest assault of the conflict to date.
Although the army held off an estimated 2,000 attackers, the analysts predicted the town would become one of two major goals of the Druze-led campaign. The fall of Souk al Gharb would put the opposition forces at the end of the Baabda suburb of east Beirut, site of the presidential palace.
The Western officials described the Lebanese Army as stretched thin and extremely tired, though morale is high.
On the political front, envoys claim the framework of an agreement has been worked out with Syria for a cease-fire that would allow rival factions to meet with the government of President Amin Gemayel in a national dialogue of reconciliation. But there continue to be hitches in Lebanon.
Syria's agreement is pivotal, due to its role on behalf of leftist Lebanese Muslims who want greater representation in the government dominated by minority Christians.
Saudi Arabia reentered the US-directed negotiations last Thursday, after temporarily suspending its involvement due to the intransigence of Syria. Prince Bandar Bin Sultan, the Saudi ambassador to the US, has become the key link man, shuttling almost daily between Damascus and Cyprus, the island off Lebanon where he meets with Wadi Haddad, President Gemayel's national security adviser.
There is tremendous pressure on the Gemayel administration to concede on Muslim demands because of the Christian and Druze civilians stranded in the Shouf. Seven massacres have been reported since fighting began nine days ago.
Questions are being raised as to who is in control, for, although the militias have sophisticated weaponry, the vast majority are not full-time fighters. Relief agencies fear the smoldering passion and fury unleashed in the mountain conflict have been difficult for leaders to contain.
There is increasing evidence that the Druzes are not fighting alone. Militiamen of several other leftist Muslim parties have been sighted in the hills, although the Lebanese government's main concern is about the role of Soviet-equipped Syrian troops and the Palestine Liberation Organization.
In what has become a daily campaign to prove the intervention of foreigners, the Lebanese government held a press conference Sunday to display three slain fighters, allegedly two Palestinians and one Syrian. One Palestinian carried a PLO identity card, and the Syrian had civilian papers, although it was impossible to verify the evidence.
Lebanese officials have repeatedly denied that the mountain war is a civil conflict, instead arguing that it is the total responsibility of external forces , mainly Syria.
But Israeli Defense Minister Moshe Arens said Friday, ''We know that the Syrians are not in the areas which the Israeli Army has vacated'' in the Shouf. He did accuse Syria of seeking to bring down Gemayel and ''allow terrorism to dominate over Lebanon and the heart of Beirut.''
Western envoys close to the peace talks contend that Damascus is increasingly playing the role of political spoiler, since the government of President Hafez Assad is making ''radical demands'' on behalf of the Druzes and other Muslims that are unacceptable to the Lebanese. The problems include whether the Army will move into the Shouf after a cease-fire, which Sunni Muslim will become prime minister to lead Lebanon toward reconciliation, and what will become of the US-orchestrated Lebanese-Israeli accord of May 17.
The Druze position has been that the Lebanese Army should not move in until after an agreement on the specific terms for new power-sharing between Christians and Muslims. And all three major Muslim sects have called for major revisions, or scraping, of the pact with Israel to disallow the residual Israeli presence after complete withdrawal of all foreign forces.
The resolution of the Lebanese crisis has not been helped by the escalation in the war of words between Syria and the US. On Sunday, Al Baath, the state-controlled paper in Damascus, charged: ''Washington is trying to blame Syria for events in Lebanon. . . . But it is responsible for what is happening here. The Reagan administration is still working on increasing tension and pushing the region to a new war.''
Meanwhile, the four-nation peacekeeping force increased pressure on forces in the mountains that have been firing at the US, French, Italian, and British troops. Although there were no attacks on the 5,200-man force over the weekend, French, US, and British warplanes swooped low over the battle zones several times. Military officials said they were on reconnaissance missions, but it was also clearly a show of strength to discourage further incidents.