Heavy fighting between Syrian peacekeeping troops and rightwing Christian militas abruptly stopped yesterday after Lebanese President Elias Sarkis threatened to resign and Israeli jet fighter planes whipped low over Beirut.

Both moves were reportedly aimed at forcing end to the heavy Syrian shelling that has killed about 200 persons and injured more than 500 in Beirut's Christian areas during the last six days.

The Syrians, getting ever deeper involved in Lebanon's complex political problems, have been trying to bomb the Christian militas into making concessions that would sharply reduce their domestic power and strengthen Syria's influence in the country.

Fighting raged again yesterday morning in Christian East Beirut after a nigh of the fiercest Syrian shelling so far. The Phalangist Radio said 1,260 Syrian shells had hit Christian sectors of Beirut overnight, setting 40 buildings on fire.

As the level of fighting began to build, Israeli jets cracked the sound barrier in low swoops over the capital.

The loud caused booms broke windows and caused traffic accidents as the jets - variously reported to number between two and seven - screamed terrifying close to buildings in predominantly Moslem West Beirut. The panic seemed to be greater than the actual damage as frightened pedestrians and motorists scrambled for safely under the impression they were being bombed.

Syrian antiaircraft batteries belatedly opened fire on the planes after they were well out of range and in a somewhat ludicrous show of bravado south of Beirut. Palestinian and Moslem leftist gunmen sitting behind machine guns in two camouflaged pickup trucks watched the skies in case the planes returned.

The Israeli swoop, a clear warning to the Syrians to stop pounding Christian districts, seemed to have the desired effect, at least for the time being. An errie silence fell over East Beirut and by late last night the big Syrian guns were still quiet unlike any night this week.

The threatened resignation of President Sarkis also appeared to play a part in the cease-fire, the latest of many that have started in Lebanon's recent history.

Sarkis, harried by Syrian conditions to end their shelling of Beirut's Christians, told a meeting of key Cabinet ministers yesterday that he intended to resign unless Damascus withdrew its demands. The resignation threat was reported by the rightwing Christian Phalangist Party radio and confirmed by diplomatic sources.

According to political sources here, Syrian-Lebanese defense past against Sarkis order the disbanding of the Christian militas, require them to turn over their installations to Syrian peacekeeping troops, dismiss Christian rightist army officers who have cooperated with Israel and conclude a Syrian-Lebanese defense pact against Israeli attack. The demands were reportedly handed to Foreign Minister Fuad Butros, who visited Damascus Wednesday.

As news of Sarkist resignation threat spread, U.S. Ambassador Richard Parker rushed to the Baabda presidential palace to urge Sarkis to stay on British Ambassador Sir Peter Wakefield held an urgent telephone converstation with Sarkis to deliver the same message.

(In Washington, President Carter issued a statement calling for a ceasefire, and the State Department late yesterday said, "We are heartened by reports that the cease-fire in Beirut appears to be holding," The State Department also expressed pleasure that Sarkis "has postponed consideration of his resignation.")

Disarming the militias is part of the government's plan to restore its authority following the 1975-76 Lebanese civil war, but Sarkis lacks the necessary domestic power base to enforce such an order, political analysts said.

They said, however, that he can no longer tolerate the Syrian efforts to subdue the militias through bombardment of Christian civilians.

Thus Sarkis is now a cornered man, trapped all the more by having played his last gambit of threatening to resign. If Sarkis does not resign, he will have nothing left to back up his stand against Syria, the analysts said.

Meanwhile, Christian militaiamen were showing new determination not to succumb to Syrian pressure. One militiaman told reporters in East Beirut that orders are not to fire on Syrian positions in civilian areas.

"But if they leave the civilian buildings and try to adavance, we will fight to the last man," he said. "The Syrians are no longer a peacekeeping force. They're an attacking army."