Syrian peacekeeping troops pounded right-wing Christian militias in and around Beirut yesterday in the worst explosion of fighting since the Lebanese civil war that supposedly ended almost two years ago. Some Lebanese blamed President Carter's peace conference proposal for the increased fighting.

Before a precarious midafternoon cease-fire was arranged, the Syrians and Christian irregulars had exchanged artillery, tank and rocket fire in a wide arc ranging north and south of Beirut.

For the first time in the current fighting, Syrian gunners attacked positions in Mount Lebanon, the Christian heartland north of the capital where many Christian residents of Beirut have fled over the past three months to escape earlier rounds of Syrian shelling.

Unlike previous clashes, the fighting also involved ground action rather than just exchanges of artillery, rocket, mortar and machine gun fire. Witnesses said militiamen in the mountains east of Beirut blew up four trucks in a Syrian ammunition convoy with direct hits from rocket-propelled grenades. There were reports of street battles around the besieged Christian suburb of Hadath near the Beirut airport.

No exact casualty figures were immediately available, but bombardments were believed to have killed and injured scores of people - mostly civilians.

In an unusual public appeal, President Carter said he had been reviewing the "dangerous situation" with Secretary of State Cyrus Vance and called "urgently on all involved to negotiate a permanent end to the cycle of confrontations which has gone on far too long and at such a heavy cost an innocent lives."

["The fighting today was particularly destructive and it seemed to be spreading," Carter said in a statement distributed to White House reporters in Washington. "I was therefore greatly releived to learn that President (Hafez) Assad of Syria had been personally involved in bringing about a cease-fire, which is holdong now."]

Veteran annalysts suggested that the fiercences of the fighting reflected diametrically opposed reactions to Carter's proposal Thursday for an international conference to deal with the 3 1/2-year-old Lebanese crisi.

A spokesman for the Christian Phalange militis explained yesterday's clash by saying, "We suppose the Syrians want to prevent President Carter from organizing [such] an international conference."

Christian militia leaders, especially former president Camile Chamoun, long have preached the need for an international - and by that they mean predominantly Western - solution to the county's problems.

That is the heart of the Christians' ever-mounting campaign to end the nearly two-year-old presence of Arab peacekeeping forces, the bulk of whose 30,000 members are Syrian troops. The present mandate expires Oct. 26. Chamoun, for example, welcomed the Carter proposal "in principle," but said such a conference would be "unnecessary" unless it helped end the Syrian occupation.

Syria, which with American backing in early 1976 began filling the Lebanese power vaccuum, shows sign of resenting Carter's conference proposal would restrict Syria's role as a regional superpower by inviting others - especially such opponents as Egypt and Israel - as participants.

Assad apparently was worried enough by the level of fighting here Thursday to cut short a Persian Gulf tour, where he was trying to line up opposition to the Camp David agreements.

The massive Syrian firepower displayed Saturday, it is argued, is a deliberate signal by Assad to the Israelis. Israeli intervention on behalf of its Christian allies could jeopardize the Camp David agreements. Damascus would like nothing better than to have the Israelis scuttle agreements which Syria so strongly opposed.

At best, Lebanese observers greeted Carter's conference proposal with skepticism. The government of President Elias Sarkis - which wants the Arab peacekeeping troops to remain for fear their departure would reignite the civil war - is on record as insisting the it was not formally consulted about the Carter plan.

Beyond that, observers do not understand how Carter hopes to reconcile such adversaries as Syria, REfypt and Israel.

"If this were possible, we wouldn't be where we are," a government official remarked privately. "If it were possible to reconcile Israel and Syria, theLebanaon wouldn't be discussed, but rather an overall Mideast peace settlement. The solution of Lebanon's problems would be a byproduct."

In any case, howecer, the intensity of the latest fighting seemed to preclude any peaceful settlement of the differences between the Syrians and diehard Christian leaders. Moreover, some observers expressed fears that Christian shelling of residential areas of mainly Moslem West Beirut - where seven Syrian gun emplacements are located - could widen the conflict by provoking the militias' Moslem leftist and Palestinian foes into joining the fighting.

Armed guerrillas in Palestinian quarters of West Beirut ordered residents off the streets and into shelters as the sector came under the most concentrated shelling since the civil war.

The Palestinians and their Moslem Lebanese allies have stayed out of the fighting since the Syrian army entered the civil war on the Christian side in the summer of 1976. The clashes between Syrians and Christians have developed since then because, the Syrians say, Christian militias refuse to obey Sarkis and, Lebanese Christians says, Syria has designs on permanent control of the country.

The Syrians yesterday trained their heavy guns on the Christian strongholds of Mount Lebanon north of Beirut and the Metn area to the east. The command of the Syrian-dominated Arab deterrent force said it was forced to return fire from long-range field artillery the militias had set up in those areas. It said militia "inflicted heavy casualties among the Arab deterrent force units, with a harmful impact on the morale of the forces involved." The statement said militia sniping had also caused high casualties in recent days.

A statement by the Phalange Party which fields the largest Christian militia, said its units were ordered "to retaliate forcefully against Syrian military positions" and that the Syrians "have suffered heavy losses in lives and equipment."

Western military sources have estimated that more than 300 Syrian soldiers have been killed since fighting with rightists broke out in February, with three times that many wounded. Militia casualties reportedly have been relatively light but more than 400 Christian civilians are believed to have been killed under Syrian bombardment.

"The shelling is heavier than it's ever been," one Christian resident of a mountain town east of Beirut said by telephone at the height of the fighting yesterday morning. "The Syrians are using all kinds of weapons I've never heard before." As he spoke, a shell landed nearby, shattering the windows of a house next door, he said.

In the western half of the city, where most embassies and foreign residents are based, the disquieting boom of outgoing Syrian artillery echoed through the largely deserted streets. The loud ripping sound of Soviet-made multiple rocket launchers, known as "Stalin organs," also kept residents indoors until the cese-fire arranged by telephone between Assad and Sarkis seemed to take hold at 3:30 p.m.