Growing Israeli demands for a peace treaty with Lebanon are threatening President-elect Bashir Gemayel's goal of uniting this long-divided nation under the sort of strong central government that Israel says publicly is its own goal.

Israeli pressure on Gemayel to commit himself to such a treaty has intensified in almost direct proportion to the Maronite Christian's efforts to break down Moslem hostility to his rule before his inaugural Sept. 23 for a six-year term as president of Lebanon.

Acceptance of a peace treaty with Israel, however, would doom his efforts toward reconciliation with the Moslems, some of whom have accused him already of being a "pup pet" elected by the parliament last month under the pressure of the Israeli Army that has occupied half of the country since it invaded June 6.

With Moslems making up more than half of Lebanon's 3 million residents, the long-term stability of Gemayal's government will depend largely on his establishment of a working relationship with the country's Moslem leaders. Only that way can he really unite the nation that has been split into hostile camps since 1975 when Christians and Moslems fought a bitter, never-resolved civil war.

As part of his efforts, Gemayel met today with Moslem former prime minister Saeb Salam and also had an unpublicized meeting with Israeli Prime Minister Menachem Begin last week during which he reportedly stressed the need for Lebanese unity.

Gemayel emerged from the civil war as the Christians' leading political figure. Moslems have long considered him an implacable enemy.

Yet Gemayel won the election last month despite the Moslems' bitter opposition. He has since been trying quietly to assuage Moslem fears by promising to start a new chapter in Lebanese politics, burying communal enmities.

After much quiet diplomacy and secret mediation, some of it inspired by U.S. special envoy Philip C. Habib before he left Lebanon last week, Gemayel met today with Salam, a Surni Moslem who heads the so-called "Islamic Conference," an informal group of leading Beirut Moslem leaders opposed to Gemayel.

The meeting at the presidential palace took place as Israeli Foreign Minister Yitzhak Shamir renewed his government's call for Gemayel to agree to sign a peace treaty with Israel. Earlier in the week, Israeli Defense Minister Ariel Sharon warned that unless Lebanon agreed to sign such a peach treaty, he would insist that a 30-mile belt of southern Lebanon be held under some form of Israeli dominion.

Israel's presence in southern Lebanon and its threat to carve a buffer zone that would be beyond Beirut's control challenge Gemayel's hope of ruling a united Lebanon under a strong central government.

The continued Israeli occupation and its insistence on a peace treaty are the dominant issues separating Gemayel from Salam and his supporters. Ending the Israeli occupation of Lebanese territory and rejection of a peace treaty with "the Israeli enemy" were the key issues of an eight-point declaration of principles by Salam's "Islamic Conference" early this week as a basis for any discussions with Gemayel.

Despite the fact that Gemayel had established a close, secret alliance with Israel as far back as the civil war to oppose Lebanon's Moslems and their now-departed Palestine Liberation Organization allies, the new president's close adviserssay privately that he sees no great problem with the Moslems' demands. They say he is a Lebanese nationalist who believes that Lebanon should be for the Lebanese themselves and not under any foreign domination.

"The only problem we have with their list of principles," said one of the president's key Phalangist Party advisers, "is that they did not insist equally for the withdrawal from Lebanon of Syrian and PLO occupiers elsewhere in the country as they did for that of the Israelis. We want all foreign armies out of Lebanon: Israel's as well as the others."

That was the gist of the message Gemayel delivered to Israel's Begin during a secret meeting last week in Nahariya, in northern Israel. Gemayel was said here to have angered Begin by insisting that the only way he could establish a strong, united Lebanon was by refusing Israel's close public embrace.

That position had a disturbing effect on the Israeli government as evidenced by the fact that when Begin reported the secret conversation to his Cabinet the news quickly was leaked to the Israeli press. Begin expressed displeasure over the leak and Gemayel was so embarrassed by it that his office formally issued a denial that the meeting took place -- a statement that few Moslem leaders were prepared to believe.

The Israeli pressure for a peace treaty raises serious questions about the chances for the success of Gemayel's presidency even before he takes office.

Politics in Lebanon since its independence from France in 1943 have hinged on a national pact, agreed to by both Christians and Moslems, stipulating that the country be governed by an informal consensus between its two dominant, if often divided, religions. According to the pact, the presidency always goes to a Maronite Christian while the prime ministership is reserved for a Sunni Moslem. The speaker of the National Assembly is a Shiite Moslem.

Although Gemayel has said often that the country must transcend this archaic tradition of dividing power and government jobs among its religious groups, the reality in Lebanon dictates that if Gemayel is to rule successfully, he must have the support of the Moslems, who are the dominant religion.