JERUSALEM (AP) _ With one candidate accused of womanizing and another of paying bribes, the election campaign for Israel's chief rabbis is under way, and it isn't pretty.

The fight for the posts of Israel's two chief rabbis has become so rough that some Israelis are saying the election should be put off. Others believe it has raised questions about the very existence of the Chief Rabbinate.

''If you want another example of the decline of the moral climate of Israeli society, this is it,'' lamented Tel Aviv Mayor Shlomo Lahat.

''We are shocked and disgusted at the depths to which the so-called 'election campaign' for the Chief Rabbinate has sunk,'' said a statement in Wednesday newspapers signed by 29 leading rabbis.

The election is not the only event that has been showing Israeli rabbis in a poor light.

Tape recordings have emerged of sermons in which Ovadiah Yosef, a revered sage and former chief rabbi, is heard cursing his opponents and urging disciples to rejoice on the day Education Minister Shulamit Aloni dies. Mrs. Aloni is a crusader for secular rights.

The secular population is still chuckling at the exploits of Chabad, a New York-based orthodox Jewish community which had plastered the country with billboards heralding the imminent arrival of their leader, Rabbi Menachem Mendel Schneerson, as the Messiah.

Came the promised day and nothing happened.

The mudslinging, the Yosef tapes and the Chabad extravaganza have dominated the Israeli airwaves in recent weeks. While treated on the surface with mild humor, they have cumulative effect of widening the gulf between the secular majority and the religious communities.

Secular Israelis resent the rising power of the religious. The religious fear secularism as a force that is diluting Israel's Jewish character. And because rabbis and secular socialists share power in Prime Minister Yitzhak Rabin's coalition, each fuss and scandal has the potential to undermine the government.

Unless postponed, the rabbinical elections will be held Tuesday, assembling 150 religious and secular public figures to choose the chief Ashkenazi and Sephardi rabbis to officiate for Israel's European- and Middle East-descended Jewish communities.

During the race for the Ashkenazi post, the Tel Aviv newspaper Ha'ir quoted unidentified women as claiming that contender Israel Lau, the popular chief rabbi of Tel Aviv, tried to seduce them when they turned to him for assistance.

Lau's camp claims the allegations were fabricated to force him from the race. Lau's followers accuse his rival, Rabbi Shaar-Yashuv Cohen, of planting listening devices in the Tel Aviv Rabbinate where Lau officiates.

A candidate for Sephardi chief rabbi, Eliahu Bakshi-Doron, has faced the resurrection of unproven allegations that he paid bribes in the 1980s to win the post of chief rabbi in the northern city of Haifa.

The chief rabbis, elected to a 10-year term, have the final legal say on matters concerning marriage and divorce, which bind all Israeli Jews. They also enforce the kosher laws.

Their leadership stature has fallen over the years as growing ultra- religious communities turn to the guidance of their own rabbis.

Thus Schneerson, not the chief rabbi, is the undisputed leader of the Chabad community, while Yosef holds sway over the Sephardi grassroots.

Left-wing lawmaker Avraham Poraz, who has introduced legislation to abolish the Chief Rabbinate, says the election mudslinging helps his argument.

''I advocate the separation of religion and state,'' Poraz told Israel radio. ''Jews have no concept of papacy. We have no hierarchy where some rabbi comes along and says he is the Jewish pope.''

But Uzi Baram, the acting religious affairs minister, says the disappearance of the state rabbinate will clear the stage for extreme rabbis to take over.

''At least now we have a Chief Rabbinate that tries to see the interests of the wider public even if it fails occasionally,'' said Baram, a secular Jew.