The fate of the next government of Israel hinges on an august body of 13 luxuriantly bearded and elderly men called the Council of Torah Sages.

The Council of Sages, a court composed of revered rabbis, religious school heads and scions of Hasidic dynasties, is the governing body of the ultra-orthodox Agudat Yisrael Party, which holds the key to the formation of a coalition government by either Prime Minister Menachem Begin's ruling Likud Party or the opposition Labor Party.

Neither the Likud nor Labor is likely to be able to form a government without the six Agudat Yisrael members of the Knesset who were elected Tuesday. According to incomplete returns, Labor won 49 seats and the Likud 48, but still uncounted ballots from the armed services are expected to create a deadlock. Sixty-one votes in the 120-seat Knesset are needed to form a government, and almost any combination that reaches that magic figure includes Agudat's six.

Agudat is in negotiations with Begin and other Likud leaders, presenting demands for concessions on future social legislation that affects Orthodox observance, and the Council of Torah Sages will decide whether the party should remain in a Likud coalition or return to one under the Labor Party as it traditionally did before Labor was ousted by Begin in 1977.

Agudat leader Menachem Porush said today his party is making two major demands:

An end to all exceptions granted to Jews for work on the Sabbath, except those involved in security work.

Resolution of the controversial "who is a Jew" issue so there will be official recognition only of Orthodox conversions to Judaism.

Following initial contact with Likud leaders, Porush said he was confident a coalition agreement could be reached. However, the Labor Party was also talking with Agudat leaders with long-shot hopes of forming a coalition.

Labor would also have to win the support of the National Religious Party and several small left-of-center, one-member factions as well as gain the passive support of the small Communist-dominated Democratic Front for Peace and Equality.

To win over the religious parties, Labor would have to drop its longstanding opposition to conservative legislation on such other issues as abortions and autopsies -- both opposed by Orthodox Jews -- and would have to take a more hard-line stand favoring Jewish settlement in the occupied West Bank and Gaza Strip.

Likud has been closer to the religious parties on the issue of settlements, and Begin has indicated he will be flexible on the social legislation effecting Orthodox observance, thereby giving Likud a decided advantage in the coalition negotiations.

The Torah sages, who range in age from 65 to 80, are expected to meet in the next week or two to discuss the coalition options.

Agudat Yisrael was created in Europe 79 years ago to defend orthodoxy at a time when Jewish youths were moving into the reform movement or secular groups such as the labor movement and Zionism.

During the Jewish migration to Palestine before the creation of modern Israel, the alienation of Orthodox Agudat Yisrael followers and secular Zionists became so bitter that Agudat leader Jacob Israel de Haan was assassinated in 1924 for attempting to come to terms with Arab nationalists.