Prime Minister Menachem Begin today began the arduous process of forming a coalition government around his ruling Likud Party in order to overcome his slight electoral deficit in yesterday's parliamentary elections.

Despite attempts by opposition Labor Party leader Shimon Peres to do the same thing, Begin appeared to be in the best position to put together a thin, 63-seat majority in the 120-member Knesset (parliament) and form a Cabinet, albeit a weak one that could be susceptible to collapse within a few months.

Based on projectons from about half of the 1.9 million votes cast, the Labor Party appeared to have won 49 seats, with the Likud winning 48. The pivotal religious parties, the Agudat Yisrael and the National Religious, appeared to have won five and six seats respectively.

National Religious Party leader Yosef Burg, after meeting today with Begin, declared: "There is reason to believe that the existing framework of a coalition between the religious parties and Mr. Begin's party will continue to exist."

Official tabulation of the paper ballots will not be complete for several days, election officials said.

Coupled with the three seats of the ethnic Tami Party of Religious Affairs Minister Aharon Abu-Hatzeira, the religious parties' seats would be enough to return Likud to power. Begin's coalition Cabinet, facing defeat in a vote of confidence last January, called for yesterday's election four months before the Likud's four-year term was to expire.

If Begin makes the coalition agreements that he has indicated he will, the religious parties, which paradoxically had their poorest showing in years, would be in a position to exert unprecedented influence on such issues as social legislation and increased Jewish settlement in the occupied West Bank and Gaza Strip.

A number of political observers said they doubted that the Likud would be able to withstand the political pressures from within for very long, and predicted that another election may be necessary in six months or less.

Former justice minister Shmuel Tamir, of the now-defunct Democratic Movement for Change party, said, "I served in a government which had the backing of 63 Knesset members, and it was very difficult to operate. A government backed by a majority of three, two or one is open to various pressures from groups within the government. It's not a stable situation."

Even some Labor Party campaign officials suggested that Peres would be wise to let Begin form a weak coalition built around his minority party. Begin would then have to deal from a weak power base with such volatile upcoming issues as the inflation spiral and the final withdrawal of Jewish settlers from the remaining occupied section of the Sinai Peninsula, which is to revert to Egypt next April.

"Let him stew for a while in the troubles ahead, and we'll come back in another election stronger than ever," said one Labor strategist, who asked not to be identified. Peres today called for a moratorium on party statements about coalition agreements until the final results are released.

The National Religious Party has been part of every Israeli government, including 30 years of Labor-led coalitions.

The orthodox Agudat Yisrael Party, which is more moderate on national security issues, has also indicated a preference for the Likud, although a preference for the Likud, although its chairman, Rabbi Pinhas Menahem Alter, said he would discuss coalition arrangements with both Likud and Labor. Alter said Agudat's primary concern is religious issues, and "Premier Begin has honored all his undertakings to us. In the past, when we had agreements with Labor, there were always difficulties."

In Israel, where there is no direct election of a government, voters cast their ballots for lists of 120 candidates to the Knesset, with the vote apportioned to the top-listed candidates of a party. Then, political parties with seats in parliament negotiate formal coalition agreements, extracting ideological and practical concessions in exchange for their support.

Both Begin and Peres scheduled meetings tonight with Burg to start discussions on possible coalition arragements.

Abu-Hatzeira, as well, has expressed a strong preference for the Likud, although Begin would have to iron out bitter divisions between Abu-Hatzeira's Tami faction, a splinter of the National Religious Party, and Burg.

It appeared unlikely that the Labor Party could succeed in concocting a similar blend of ideology and political arithmetic to form a ruling coalition.

Theoretically, Peres could form a government by winning over Agudat Yisrael, lumping together three left-of-center one-member parties, recruiting former foreign minister Moshe Dayan and winning the passive support of the Democratic Front for Peace and Equality, a four-seat Communist list. That would give Labor a coalition with 62 seats, one more than necessary, although the Communist list would not be included in the government since it is regarded as a non-Zionist party.

Nevertheless, despite Peres' claim that Labor "got a mandate to form a government," Likud Party advisers said it is only a matter of time before they have lined up a unified front of religious parties to support Begin.

"The lines of the coalition are clear. It may take a while, but we have a coalition," said David Garth, a New York-based political consultant who advised the Likud campaign.

The process of forming a coalition could take months. The president, Yitzhak Navon, is obligated to consult with the political parties winning Knesset seats. Traditionally, the president consults all the parties to determine which are capable of forming a coalition.

Navon will then ask the leader of one party to attempt to form a government. The assumption is that he will ask the largest party because it could be expected to have the best chance of winning an initial parliamentary vote of confidence. But there is nothing in the law to preclude him from going to another party.

The potential coalition leader is then given 21 days to form a government, with a further 21-day extention if necessary. If the party leader fails to form a government, the president can go to another party and ask it to try. In the event of repeated failures, new election can be called.

It remained unclear tonight whether Navon would go first to Labor, which is his own party, to give it a chance to form a government, or to Likud, because of its natural religious-parties coalition partners. Navon said only that he will not even start consulting the Knesset factions until the final tabulations are in.