The shooting war between Syrian peacekeeping forces and Lebanon's Christian militias gave way to a war of words over the weekend, but the lastest crisis afflicting this prostate country continued with no sign of a solution.

Syria appears determined to impose its will on the Christians, to end the military independence and political defiance that have made them a state within a state.

Leaders of the major Christian parties and of their militias continued to proclaim their determination to resist, and President Ellis Sarkis, caught in the middle, left his resignation threat up in the air, neither withdrawing it nor carrying it out.

A tenuous and unofficial cease-fire remained in force yesterday, but the streets of Christian East Beirut, littered with rubble, glass and burned vehicles, remained nearly deserted as sporadic small arms fire continued.

There was every sign that the cycle of death, destruction, waste and human suffering that has broken Lebanon in the past three years will continue. Numbed and weary Lebanese journalists and politicians said privately that it appears to make little difference whether Sarkis resigns or not. The latest round of fighting, like the civil war and the Israeli invasion of the south that preceded it, has not settled the power struggle between the Christians, who traditionally have dominated the government despite their diminishing numbers, and the Moslems, whose political power has not grown as fast as their numbers.

With their areas of Beirut and the coast to the north surrounded by Syrian troops, Christian spokesman admitted that their people are short of food, medicine and supplies. Refugees from the city have sought shelter from monasteries and convents.

But the militias of the main Christian parties remained at their posts. Estimated to be at least 10,000 men on full-time duty, they clearly were not crushed by the hurricane of artillery fire that Syrians unleashed on them last week.

Beirut newspapers yesterday reprinted warnings from the official Syrian press that Damascus government of President Hafez Assad, whose army is the only real power behind Sarkis, was determined to break the power of the Christian parties and force them to submit to the central government that Syria has been trying to establish here for nearly two years.

In a typical comment, the Damascus newspaper Tichrin said that "Syria can no longer tolerate the arrogance of these parties."

Syria's information minister, Ahmed Iskander, said in a radio interview yesterday that the Christian parties - the National Liberal Party of former president Camille Chamoun and the Phalange of Pierre Gemayel - must submit to the authority of Sarkis "or be destroyed."

But the Christians have recruited new troops and have proposed from an unofficials alliance with Israel while Syria was bringing the Palestinians to heel in an earlier round of the struggle here. They have showed no inclination of bowing to the Syrians.

Chamoun said two days ago that "there can be no compromise whatever: The Syrians have to get out." He is showing no sign of changing that position.

Gemayle, who has a reputuation as a more pragmatic and flexible figure than Chamoun, was more conciliatory, urging a return to the voice of reason" issuing a statement saying, "We want no antagonism with Syria." He too, said, however, that the Syrians will have to leave in three months when the mandate of the multinational Arab peacekeeping force, which gives the Syrian Army its cloak of legality here, expires.

Syria would like to pull out the estimated 30,000 troops that it has had tied down in Lebanon for the past two years, but Assad has said he will not do until order is restored here under the authority of a central government.

Sarkis is the key to that, and since he was unable to extend his writ into the Christian zones of control by himself, the Syrians apparently sought to do it for him.

The Syrian troops halted their bombardment of East Beirut Thursday when Sarkis, who is a Christian, threatened to resign over the Syrian tactics and the Israelis threatened to intervene. Now, according to informed observers among the Christians, Syria is trying to do indirectly what it was trying to do militarily.

Syrian troops are chipping away at the areas of Lebanon under the control of the Christian militias and strangling East Beirut with a view, the Christians say, to obliging the militias to disband and the party leaders to accept Sarkis' authority. If Sarkis resigns, observers here say, the Syrian program would be the same under whoever succeeds him.

Sarkis became president with Syrian backing, but it appears that his threat to resign has changed only Syrian tactics, not Syrian objectives.

His authority could become real instead of theoretical only if Syria allowed him to command the Arab peacekeeping force in fact as well as on paper, and if the leaders of the Christian factions allowed his writ to extend into their fiefdoms. Neither appears imminent.

The foreign minister of Kuwait, Sheikh Sabah Ahmed Sabah, came here yesterday after a stop in Damascus, apparently on a mediation mission. He was quoted as saying that "the Lebanese should solve their problems by themselves although the Arabs will always help them to solve other problems," a cryptic observation that was taken to mean he had accomplished little.

There is an odd parallel between the situation in Christian-dominated East Beirut today and Palestinian-dominated West Beirut during the civil war.

The Syrians, who tried to bludgeon their way into the Palestinian zones and found out the price would be too high militarily and politically, turned to a campaign of squeezing the Palestinians into submission by closing their supply lines and pressuring their leadership.

That appears to be what is happening in the Christian zones now, but whether it will work against determined fighters who are in their own country and have the logistical support of Israel is open to question.