JERUSALEM — As Israeli and Palestinian leaders cut through decades of sacred axioms and slogans in an effort to forge an agreement at Camp David this week, Israeli society dealt with the possibility that it may face the toughest-ever challenge to its cohesion.

The summit appeared all but over Wednesday night until Prime Minister Ehud Barak and Palestinian leader Yasser Arafat decided to continue their talks without President Clinton, who left for the G-8 economic summit in Japan.

With the sudden decisions to continue the talks, both leftists and rightists in Israel were planning counter demonstrations. Last Sunday, hundreds of thousands of right-wing Israelis demonstrated in Tel Aviv's Rabin Square against Barak's peace policy. Further protests were planned later this week. Meanwhile, hundreds of thousands in the left-wing camp were planning a demonstration for this coming Sunday to support Barak.

When the summit finally ends, the embattled prime minister returns to a changed political landscape. Three coalition parties pulled out of the government prior to his departure for Washington, costing him his parliamentary majority.

In two weeks, the Knesset is scheduled to vote on two bills that would force early elections.

And in a taste of what may come, the Knesset on Wednesday gave preliminary approval to two opposition initiatives. The first would require a special majority to approve a national referendum on any peace agreement. And the second calls for the annexation of all Jewish settlements in the territories if the Palestinians unilaterally declare an independent state.

No matter what emerges from Camp David, the future of Israeli-Palestinian relations are likely to continue to rock Israeli society.

Possible provocations by extremists is now a major concern — and will be if there is a peace referendum or if the Palestinians declare statehood.

The extremists, either Israeli or Arab, could instantaneously turn the West Bank into a raging conflagration.

In that respect, Jewish and Palestinian extremists are, perhaps paradoxically, in the same camp — the anti-agreement camp.

Violent altercations between them, or acts of violence perpetrated by either of them against innocent civilians, are the great danger that will loom over any agreement.

A mild taste of what could come was experienced over the weekend in the West Bank town of Hebron. Jewish settlers and local Palestinians clashed for two days after a settler girl claimed a Palestinian sexually assaulted her.

The army was slow to move in and separate the two sides in the tinderbox town. There were no fatalities, although some injuries were sustained by Palestinians, settlers and soldiers.

Had there been any fatalities, the rioting could quickly have spread to engulf the whole town.

On another front, observers point to large pockets of deep distrust of Arafat among the Palestinian populace — in addition to the consistent opposition led by Sheik Ahmed Yassin, the spiritual leader of Hamas.

The sheik this week issued a call to Arafat to break off the talks, return home and rejoin the armed struggle against the Zionist state.

There could be no real solution to the conflict, Yassin asserted, other than the elimination of Israel.

No such incitement has been uttered publicly on the Israeli side. But Israeli security officials know there are extremists in some of the settlements, especially those Barak may be willing to cede to the Palestinians.

It almost appeared that the extremists on both sides would get what they wished on Wednesday. The summit was about to end when both sides suddenly decided to continue their talks.

Early in the day Wednesday, Barak had indicated in a letter to President Clinton he was abandoning the summit because the Palestinians lacked the "true commitment" needed "to make historic decisions."

Ophir Pines, Barak's governing coalition chairman and Labor Party Knesset member, said the premier had reached the conclusion that the Palestinians were not acting as a "true partner" to peace.

Pines said he also understood the Clinton administration had reached the same conclusion: The Palestinian Authority was not able to come to an agreement with Israel.

"All the American bridging proposals were rejected by the Palestinians," he said.

But late Wednesday night Clinton told reporters,"The gaps remain substantial, but there has been progress and we must all be prepared to go the extra mile."

The White House said bags had been marked and a departure by all parties were planned until a sudden decision was made to continue the talks.

For the past week, Israeli, Palestinian and American officials have been engaged in what was described as a final, high-stakes bid to try to reach a final peace accord.

A heavy news blackout imposed by the Americans prevented any substantive information on the content of the deliberations from trickling out. That resulted at times in simultaneous and contradictory reports on progress or deadlock in the negotiations.

On the agenda were the most difficult and contested issues of the negotiations — Jerusalem, refugees, final borders, water and Jewish settlements.

Earlier reports said Barak had conveyed his willingness to hand up to 95 percent of the West Bank to the Palestinians and was open to some proposals on the refugee issue.

But over the course of the week, Jerusalem apparently emerged as the main sticking point — representing a so-called "red line" for both sides.

Barak insisted that Jerusalem remain the united, sovereign capital of Israel. Arafat had demanded its eastern half for the capital of a Palestinian state.

Israeli reports speculated Tuesday that the sides might be on the verge of clinching an understanding on the issue — a compromise under which Israel would annex Jewish settlement areas around the city while the Palestinians would assume some sort of control, short of sovereignty, over the Arab neighborhoods of Jerusalem.

But by Wednesday, Arafat reportedly had hardened his stance on Jerusalem — which sources said had led Barak to conclude that he was not dealing with a real partner to the peace process.

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