Lebanese President Amin Gemayel, in office only two days, is fighting to stave off the potentially crippling fragmentation of his Christian power base that was forged by the ambitious determination of his assassinated brother Bashir.

With his nation still reeling from the shock of the massacre of Palestinian civilians at the Shatila and Sabra refugee camps by Christian militias last week, Israeli troops still patrolling the Moslem sector of his capital and occupying the southern half of the nation and with no new government yet formed, one of Gemayel's first priorities is the imposition of authority over the powerful Lebanese Forces Christian militia that was built--and led until just before his death--by his late brother.

Asserting control over the Christian militia, whose Israeli-trained units reportedly took part in the Shatila massacre, apparently without the president's knowledge, is considered critical to the success of Gemayel's presidency in this divided, war-torn land, whose territorial integrity the Reagan administration has committed itself to defend.

Members and leaders of the Lebanese Forces, however, have made it clear that they have no intention of allowing Gemayel to disband the militia as his brother, Bashir, had vowed to do.

"Whatever happens in Lebanon, the Lebanese Forces will remain as a military machine, the minimal guarantee of freedom in Lebanon," one senior militia general staff officer said today, asking that his name not be used.

The seriousness and difficulty of the task of bringing the Lebanese Forces under control was underlined two days ago when Israeli Defense Minister Ariel Sharon told parliament in Jerusalem that units of the Lebanese Forces -- under the command of senior officers and with the coordination and logistical support of the Israeli Army -- entered the camps, where they then killed hundreds of unarmed civilians.

Sharon's assertion, denied officially by the Lebanese Forces command, stunned the new president and officials of his rightist Phalangist Party that in the past was considered to have at least nominal control over the militia through its commander-in-chief, Bashir Gemayel.

The importance of the 20,000-strong Lebanese Forces, who have been trained and armed by Israel during the past seven years, cannot be underestimated in this fragmented land where effective government power in the past half decade has been confined to little more than a few square miles around the presidential palace in Baabda, on a hill overlooking the capital.

Under Bashir Gemayel, killed only 22 days after he was elected to the presidency, the Lebanese Forces were the real power establishment of the country's dominant Christian minority.

With the dynamic and decisive Bashir Gemayel in the presidency, Lebanese and foreign analysts say, the Lebanese Forces would not have been a major problem. The assassinated president-elect held the loyalty, respect and even love of the militiamen whom he had commanded since 1976.

Bashir Gemayel's assassination Sept. 14, in a bomb blast in a local East Beirut headquarters of the Phalangist Party, not only deprived the nation of what would have been a strong president, but also ruptured the tenuous link between the Phalangist Party, founded by his father, Christian patriarch Pierre Gemayel, and the tough nationalist militia that Bashir had built into his personal power base.

The link between the Phalangist Party and the Lebanese Forces was personal, not institutional, and was possible because Bashir Gemayel belonged to both. His death, judging by the massacre at the refugee camps, has snapped the connection. The heavily armed Lebanese Forces has been left as a powerful independent political force in its own right in the Christian heartland of Lebanon that the president will have to control or risk being controlled in turn. There is reason to believe that President Gemayel, elected and inaugurated to fill the job vacated by his brother's violent death, is aware of the need to win the loyalty of his brother's private army. No sooner had he been elected by parliament Tuesday, than he rushed down to pay a courtesy call on the Lebanese Forces' "war council" now under the command of his brother's former chief of staff, Fadi Ephraim.

The call underlined Amin Gemayel's concern about the Christian militia, some of whose units--according to Israeli sources -- and including even its elite security unit under the tough chief of intelligence Elie Hobeika, took part in the Shatila massacre that has left more than 300 men, women and children dead, with perhaps hundreds more still missing and presumed dead under still-unopened mass graves.

Although the new president, always the family's politician, had inherited his brother's presidensha many of the officers and men in Bashir's private army view Amin as a man who represents Lebanon's discredited traditional politics of accommodation, not the tough, nationalistic populism that was Bashir's attraction for them.

That Amin has not been accepted as these Lebanese Forces' new, even titular, head was made clear when word first ran through West Beirut after Bashir Gemayel's death last week that its units had been spotted entering the Palestinian refugee camp of Shatila that adjoins Saba, on the southern fringe of West Beirut.

A senior Western diplomat called Amin Gemayel, at the time a presidential candidate, and asked what was going on. Gemayel said he did not know anything about the militiamen being in the camp but would check and call back.

Fifteen minutes later he returned the diplomat's call and confirmed that Lebanese Forces militiamen were in the camp, but said they had been ordered to leave within the hour. They stayed another 12 hours, to continue the killing until the next morning.

As evidence has continued to mount over the involvement of the Lebanese Forces in the massacre--accompanied by other Christian militiamen from the forces of renegade Army major Saad Haddad--so has fear that the new president will not be able to assert the sort of control over the militiamen that his brother could.

With both the Lebanese Forces and Haddad officially denying any involvement in the massacre, the government has so far been silent, although a government inquiry has been ordered.

Details of the Christian involvement being leaked out of Israel in recent days, are devastating, if true. It was first expected that individual units may have acted on their own. But Sharon laid the responsibility for the massacre at the feet of the Lebanese Forces' high command, who he said had met with Israeli Chief of Staff Rafael Eitan and Gen. Amin Drori, the Israeli Army commander in Lebanon, to approve the militia's entry to the camps as early as last Wednesday morning, hours before Israeli forces moved into West Beirut.

Other authoritive Israeli sources have been telling journalists in Jerusalem that it was the Lebanese Forces' own chief of intelligence, Elie Hobeika, a member of the late commander's personal entourage, who led the slaughter in the camp. Others have pinpointed Anastas Dib, the Lebanese Forces' military police chief, as having been involved, explaining perhaps why military convoys were guided to Shatila through Israeli Army security positions, by signs with the Lebanese Forces' emblem next to the initials "MP."

Each new allegation--from witnesses who saw them at the camp, or moving along roads to or away from it, or coming from leaks from Israeli Army and intelligence services in Jerusalem -- has been met with embarrassed silence by both the Phalangist Party and the Lebanese Forces who have retreated behind cold, noncommittal statements that they are conducting their own investigations.

Privately party officials show signs of deep worry. Senior Phalangist Party officials today toured Lebanese Forces barracks, especially in such Israeli-controlled towns south of Beirut as Damur and Beit el Din, where some of the Christian shock troops were believed to have come from, to, as one official said today, "explain the situation to them in the wake of Bashir's death."

The party officials, acting at the behest of the new president, are understood to have sought to assure the Lebanese Forces militiamen that Gemayel will not abandon their interests and will follow the policies backed by his brother.

Senior Lebanese Forces officials, however, say privately that despite continuing talk that the forces will be demobilized at some point by the new president, they have no intention of giving up their arms or abandoning their militia.

It had been one of Bashir Gemayel's expressed intentions to build up the central government's weak and still untested regular Army in order to slowly disband the militia that had brought him to power. He had intended to do this by convincing his men of the need to establish a strong central government now that he was president and would represent their interests. He had planned to integrate those who wanted to join into the regular Army, and leave other units perhaps as a type of National Guard.

Without Bashir Gemayel in power, the Lebanese Forces can be expected to remain for an indeterminate period to ensure that his political programs and ideas are implemented.

Given the fact that the Lebanese Army, rebuilt since its collapse under the strain of the 1975-76 civil war between Christians and Moslems, is considered no match for the Lebanese Forces, that does not augur well for the new president unless he can bring his brother's former militiamen under his control, and eventually disband them as his brother intended to allow the state to fully assert its authority around the country.