JERUSALEM — The government's razor-thin majority in last week's Knesset vote signals the death of the Labor hawk — those who perched on the right edge of the leftist party.

In the 61-59 vote that came after hours of debate, two of the Labor Party's most outspoken hawks, Avigdor Kahalani and Emanuel Zismann, joined with the Likud-led opposition. In effect, they drummed themselves out of their party.

The two intend to forge a political party out of The Third Way movement — currently a grouping of politicians, professors and generals offering an alternative to Labor and Likud platforms — and to enter next year's general elections on their own terms.

The defections of Kahalani and Zismann finally wiped out the notion of Labor hawks.

For many years, Rabin himself — as prime minister in the 1970s and again in the '90s, and as defense minister in the unity governments of the '80s — was the focus of all the Labor hawks' efforts and loyalties.

He was their uncrowned leader, their champion, the man whose position in the party and in the country they strove to promote. He was the man who initially told army soldiers to "break the bones" of intifada protesters.

But that long period has irrevocably ended.

Rabin can no longer, by any stretch of the imagination, be classified as a hawk within his own party.

Indeed, Labor no longer has any hawks.

The doves — men such as Yossi Beilin, Avraham Burg and Uzi Baram, who saw Foreign Minister Shimon Peres as their ideological leader — are now in the mainstream.

Those identifying with the hawks have had to toe the party line — or leave with Kahalani.

The final confirmation of this sea change within Labor was Rabin's remark, deliberately timed to coincide with the final negotiation of the interim agreement, that he no longer necessarily rules out a Palestinian state sometime in the future.

He later tempered that statement, saying that it would take "50 years" for the Palestinians to accomplish that goal.

But the number of years it will take is a question of degree. The core issue — partitioning Palestine and agreeing to Palestinian rule over part of the land — has been resolved as far as the Labor Party is concerned.

The battle with the Likud and its allies is now, as never before or since the 1967 Six Day War, clear-cut and unequivocal.

Rabin's wafer-thin Knesset majority may not last until the end of the Knesset's current term. Another spate of terrorist attacks could terminally sap the government's standing among the Israeli public and lead to its downfall.

But the prime minister, with eminent political soundness, is pressing ahead with his peace policy as though he had no parliamentary care in the world.

His purpose is two-fold:

*To fortify the irrevocability of the terms of the interim agreement, by implementing the Israel Defense Force's redeployment from the main Palestinian population centers in the West Bank and then, next summer, extending Palestinian rule to some unpopulated areas of the West Bank.

*With each advance in the peace process, to throw the rightist opposition further and further on the defensive, by pointing up the widening gap between the right's political ideology and the practical situation on the ground.

In an effort to move forward with the peace process, and with facts on the ground, Peres and Palestine Liberation Organization leader Yasser Arafat met Saturday night at the Erez Crossing between Israel and Gaza to finalize details of the timetable for the IDF redeployment in the West Bank.

Peres told Arafat that Israeli troops would redeploy from four West Bank villages in the coming weeks and that the Israeli army would withdraw from six West Bank population centers by December.

With Yasser Arafat and his Palestinian Authority governing from the West Bank town of Ramallah — as they are scheduled to be by the start of 1996 — Rabin will be contending in the election campaign that only he has a policy tailored to the new realities, which, after all, he himself shaped.

The Likud's policies, Rabin will argue, are no longer relevant to the situation currently existing in the West Bank.

Likud leader Benjamin Netanyahu will be hard put to respond with a platform of his own that addresses this new reality on the ground and maintains the basic tenets of the Likud's "Greater Israel" ideology.

In this scenario, Rabin's electoral fortunes, and the interests of the peace process itself, will be served by the speed and extent that he can push the process forward in the months ahead — despite the arithmetical fragility of his coalition government.

Yet Rabin also runs a more unified party now free of the hawks he once led.