A police investigation into alleged bribery and corruption in the Religious Affairs Ministry has deeply divided the pivotal National Religious Party, threatening to undermine the fragile Likud coalition of Prime Minister Menachem Begin.

While no allegations have been substantiated in court, relentless attention to the affair by Israel's press has shaken Begin's Cabinet and raised far-reaching questions about not only the current coalition government's stability, but about the ability of any alliance of parties to form a new government without a united Religious Party.

Attention so far has focused on Religious Affairs Minister Aharon Abuhatzeira, who is at 40 the youngest member of Begin's 18-member Cabinet and a scion of a prestigious Moroccan-Israeli family with broad influence in the Sephardic (Oriental) community that comprises nearly half of Israel's population. Sephardic Jews, many of them from North Africa, were instrumental in the election of Begin in 1977.

The investigation entails the most serious allegations brought against a Cabinet minister since 1977 when Avraham Ofer, the housing minister at the time in prime minister Yitzhak Rabin's government, committed suicide during an investigation into the diversion of funds from a housing corporation owned by the Histadrut labor union federation.

Abuhatzeira has denied any improprieties and accused the national police of "intentional leaks meant to blacken" his reputation. He said the affair was designed to weaken the Sephardic faction of the National Religious Party.

Abuhatzeira and six close associates reportedly are being investigated on suspicion of funneling hundreds of thousands of dollars of Religious Affairs Ministry funds to nonexistent religious seminaries. Some of the money, Israeli newspapers have reported, turned up in Swiss bank accounts of some of the persons being investigated.

A Tel Aviv magistrates' court issued travel restrictions against six persons connected with the case after, it was reported, three of them left the country.

Interior Minister Yosef Burg, head of the mainstream faction of the Religious Party, has come under increasing criticism for permitting a "witch-hunt" of Abuhatzeira and his associates by the national police, which Burg's ministry controls.

Burg last week angrily walked out of a meeting at party headquarters when members accused the head of the national police fraud division, Binyamin Seigel, of "destroying careers" and launching a "concerted attack on the Oriental communities' leaders."

Traditionally, the Israeli national police has used the freewheeling Israeli press to pressure suspects in white-collar crimes into implicating themselves publicly, and this investigation appears to be no exception.

Detailed leaks of allegations made by witnesses to police interrogators have appeared almost daily under banner headlines, most notably involving Yisrael Gottlieb, acting mayor of the Orthodox Jewish community of Bnei Brak, a suburb of Tel Aviv.

Gottlieb, who authorities said will be a witness for the prosecution in exchange for immunity, reportedly has told police that he transferred large amounts of Religious Affairs Ministry funds earmarked for Bnei Brak religious schools back to Abuhatzeira at the minister's request. Scores of other religious schools that never existed were said to be involved in the transfers, the most recent concerning the alleged allocation of $9,000 on May 20 to a nonexistent institution.

Similar transactions, according to press reports attributed to the police and never denied by the national police authorities, extend to three years ago, when Abuhatzeira took office after serving as mayor of the city of Ramle.

Moreover, Israeli newspapers, quoting police sources, said that Gottlieb gave Abuhatzeira receipts for the funds marked with the forged rubber stamps of existing and ficticious religious institutions, and that other persons receiving money posed as officials of nonexisting schools. The police have raided Religious Ministry offices to collect evidence in the case.

So far, Burg, who is also Israel's chief Middle East peace negotiator, has sought to distance himself from the affair, and Begin has confined his reaction to better attacks on the Israeli news media for trying the case publicly before indictment.

The key questions arising from the Abuhatzeira affair are what effect it will have, regardless of its outcome, on the Religious Party, and how it will effect Begin's Likud coalition, which has a thin, two-vote majority in the 120-member parliment. With 12 members in parliament, the Religious Party could become so divided between Abuhatzeira's Sephardic faction and the two other factions -- led by Burg and Education Minister Zevulun Hammer that the coalition would collapse.

On the other hand, all elements of the party realize that in order to survive politically and remain viable as a coalition partner in any government, the party must remain united or the religious community's representation will be on the sidelines of power.

So far, the opposition Labor Party has restrained itself from fueling the controversy, because it realizes it may need the Religious Party to form its own coalition government after the next elections, just as all elected party alignments have since the founding of the state in 1948.

"They're in there fighting in the dirt, but you don't see anyone standing around cheering. There's too much at stake for that," said a Likud political strategist.

Meanwhile, in keeping with Israel's rough-and-tumble style of politics, purported evidence against Abuhatzeira continues to dominate the newspapers, with scarcely a suggestion that it may prove unfounded.

At a reception last week in his home town of Ramle, which happens to be site of Israel's largest prison with the same name, a supporter stood up and assured Abuhatzeira, "There will always be a place for you in Ramle."