Lebanon's powerful Christian Phalangist Party has endorsed "in principle" a plan by President Amin Gemayel to extend the control of the regular Lebanese Army to Christian East Beirut and surrounding suburbs where the Phalangist Lebanese Forces private militia has ruled for more than seven years.

If implemented, the regular Army's presence would be extended to the foothills of southern Beirut, including areas that are now controlled by Israeli troops and are the scene of continued fighting between Christian and Moslem Druze militiamen.

Agreement on the plan followed months of delicate negotiations between Gemayel and his fellow Maronite Christian leaders over what has been regarded here as essential to any chance the 40-year-old president may have of putting back the pieces of this war-devastated nation.

The agreement comes after reports that Israeli Defense Minister Ariel Sharon last week warned that Gemayel could not survive if he did not cooperate more with Israel. In that sense, the agreement may be an effort by Gemayel to display his independence of Israel.

Many here are skeptical that the plan will be carried out because the Lebanese Forces would have to make significant concessions. But even if it is, it would be only the first step in the complex process of dismantling the state-within-a-state that Christian militias erected after the collapse of central goverment authority in the years of war here.

It was understood that Gemayel's agreement with the Phalange would still permit its private militia, the Lebanese Forces, to keep arms, but not appear on the streets with them. Lebanese Forces leaders have contended that the militia must continue to exist as a separate entity until all foreign forces leave and the regular Army is strong enough to take control.

Western military experts estimate that it will take two years or more to rebuild what one American general recently described as a "hollow army."

After he was suddenly elected last September following the assassination of his president-elect brother, Bashir, Amin moved swiftly to disarm the roughly 40 militia groups reigning over predominantly Moslem West Beirut.

His failure to take the same action in Christian East Beirut was increasingly jeopardizing the support he had gained from Moslem leaders. Some of them had begun tauntingly calling him the "president of West Beirut," referring to the continued occupation of Lebanon by Syrian, Israeli and Palestinian troops and the dominance of East Beirut by the Lebanese Forces.

In the tangled politics of this nation, Gemayel's negotiations to extend control of the Army to Christian areas of the capital and its suburbs have involved difficult dealings with leaders of the Lebanese Forces, which was created by Bashir, and the Phalangist Party, which is headed by his father Pierre.

Although the Lebanese Forces gave lip-service support to Amin Gemayel after his election, their emotional attachment remained with Bashir, whom they have immortalized in billboard-sized oil paintings along freeways and above commercial streets of East Beirut.

Several officers in the Lebanese Forces have responded more to the direction of the Christians' de facto ally, Israel, than to Amin Gemayel who has sought to maintain ties with the Arab world that is so vital to the banking and trader economy of Lebanon.

The leanings of Amin's father have been less easy to discern. It used to be, said sources close to the Phalangist Party, that when Pierre Gemayel was with his son he defended the Lebanese Forces--and when he was with the Lebanese Forces he defended his son.

But Pierre Gemayel appeared to have gotten his dander up after Sharon attempted to pressure him and issue warnings to his son to agree to Israel's conditions for withdrawing.

The elder Gemayel vented his anger in an interview with the leading leftist newspaper here, when he appealed to Moslems and Christians to end their differences in order to avoid being "dragged" under the control of Israel.

"Don't force the Christians to go with them," he pleaded. "They are doing their best to drag us with them. It is not in our interest to divide Lebanon . . . The Moslems must understand this because they and we will lose Lebanon."

Gemayel recounted that he had told Sharon the Christians "are not alone in this country. Listen to me, it is in your interests not to divide Lebanon. The Lebanese interest dictates that we Lebanese stick together--not with Syria, not with the Palestinians, not with Israel."

[Meanwhile, an advance unit of 22 British soldiers, members of the Queen's Dragoon Guards, arrived in Beirut today to join the 4,400-man multinational peace-keeping force, The Associated Press reported. Seventy-eight more British troops are due next Tuesday to start a three-month tour.]