A right-wing party delivered Ehud Olmert the most overt domestic rebuke yet to his attempts to seek a peace deal with the Palestinians by quitting the prime minister's coalition government.

The pullout of the Yisrael Beiteinu party announced Wednesday comes just two weeks before what might be an even tougher challenge to Olmert: the publication of the final report on his handling of the 2006 Lebanon war.

Yisrael Beiteinu leader Avigdor Lieberman described his departure as the actualization of a longstanding threat to leave Olmert if he were to open final-status negotiations with Palestinian Authority President Mahmoud Abbas.

Those talks began last week during President Bush’s visit to the region, with the implication that Abbas may achieve Israeli concessions on so-called "core" Palestinian demands: a state in all of the West Bank and Gaza Strip, shared sovereignty in Jerusalem, and a right of return for Palestinian refugees to Israeli territory.

That is all anathema to Yisrael Beiteinu, which argues that the Jewish state should annex West Bank settlement blocs and in their stead cede Israeli Arab towns to the future Palestine’s jurisdiction. To do otherwise, Lieberman said, would be to encourage pro-Palestinian irredentism within Israel.

"Those who say that the reason for the conflict is over territory, over settlements and outposts are simply deluding themselves and others,” Lieberman said at a news conference after tendering his resignation to Olmert. “For us, this principle of territories in return for peace is invalid. The guiding principle must be an exchange of territory and of populations."

"It's not that we're against the solution of two states for two peoples," Lieberman added. "On the contrary, we support it: two states for two peoples, not a state and a half for one people and half a state for the other."

Lieberman's departure is not an immediate threat to Olmert. Even shorn of Yisrael Beiteinu, the Israeli coalition government still controls 67 of the Knesset's 120 seats, enough to survive no-confidence motions and enact key legislation.

More liberal members of the coalition likely will not miss Lieberman, a Moldovan-born former nightclub bouncer whose nationalist rhetoric often raises Arab hackles. Israeli hawks, too, had looked askance at Olmert's decision to grant Lieberman, who lacks a defense pedigree, the Cabinet portfolio of minister for strategic affairs.

Responding to news of Lieberman’s resignation, Olmert’s office released a statement saying, "The prime minister is determined to continue the diplomatic negotiations out of recognition that they contain the only real chance to assure the peace and security of Israel's citizens."

But political analysts say Olmert is concerned that Yisrael Beiteinu's move could prompt Shas, another right-wing party in the coalition, to quit, too.

Shas, whose constituency is Sephardim, many of them fervently Orthodox, has said it will quit if Olmert opens discussions on ceding parts of Jerusalem to a future Palestinian state. Israel's Channel 10 TV reported that the prime minister assured Shas that Jerusalem "is not on the agenda for now.”

Another wild card is the center-left Labor Party, Olmert's biggest coalition partner.

Labor's leader, Defense Minister Ehud Barak, hinted before joining the government last year that he was ready to leave if the commission of inquiry into the Second Lebanon War faulted Olmert and Olmert refused to step down.

The Winograd Commission is due to publish its second and final report on Jan. 30, following up on interim findings that described Olmert's handling of the 2006 offensive against Lebanese Hezbollah guerrillas as inexpert and hasty.

Olmert has denied wrongdoing and pledged to stay in office.

A split between Labor and Olmert's centrist Kadima party would be certain to topple the government and trigger new elections -- a potential boon for Barak, a former prime minister who wants to retake the nation's helm.

By the same token, early elections in the shadow of the escalating conflict in Gaza -- 19 Palestinians were killed in fighting with Israeli troops there on Tuesday, the highest single-day Palestinian casualty figure for months -- might play into the hands of center-right opposition leader Benjamin Netanyahu, of Likud, whom polls show leads the race to be the next prime minister.

Surveying the political landscape Eitan Haber, the erstwhile aide to Yitzhak Rabin, wrote in Israel’s daily Yediot Achronot, "A tragedy is unfolding before our eyes."

"At a tough time for the State of Israel (and cynics will say, when hasn't it been a tough time for the State of Israel?), and at a time when the government is broad and supported by almost a record number of parliament members, it is about to fall apart just because Avigdor Lieberman promised to take it apart if the prime minister tackles core issues (Jerusalem, refugees and others) and Ehud Barak promised to defect to the opposition when the second Winograd Committee report is published.” Haber wrote.

For now, ordinary Israelis are more preoccupied with cross-border violence from the Gaza Strip, which inflicted new damage in Sderot this week and left one man in Israel dead when Palestinian terrorists fired guns across the border fence. The victim was a 20-year-old volunteer from Ecuador, killed as he worked a field in Kibbutz Ein Hashlosha, a few hundred yards from the Gaza border.

Israeli forces raided a Hamas stronghold east of Gaza City on Tuesday, killing 19 Palestinians, most of them gunmen. Airstrikes continued Wednesday and a senior Islamic Jihad terrorist was killed by Israeli commandos in the West Bank.

Another airstrike east of Gaza City that targeted the chief rocket maker of the Popular Resistance Committees terrorist organization instead hit a similar-looking vehicle, killing a 12-year-old Palestinian boy, his father and his uncle.

Hezbollah chief Sheik Hassan Nasrallah, a self-styled expert on Israeli political affairs, posited that Olmert had ordered the crackdown in Gaza has part of his efforts to distract the public from the imminent Winograd report.

"I urge our brothers in Gaza to be cautious -- even the political leaders of Hamas are not now immune" from Israeli attack, Nasrallah told followers in Beirut.

Nasrallah's theory was echoed by Hamas' supreme leader, Khaled Meshaal, in Damascus.

“Lieberman has left the government and Shas is also considering doing so, and the Palestinians are paying the price," Meshaal told reporters.

Then he turned to Israel's Achilles heel in Gaza: Cpl. Gilad Shalit, the Israeli soldier held captive there for more than 18 months and whose return Hamas has offered in exchange for 1,400 jailed Palestinians.

"I tell the enemy: What you're committing will deprive you of anything you're betting on. There will be no exchange involving Gilad Shalit, no calm or nothing of this sort," Meshaal said.

One of the Palestinian gunmen killed Tuesday was a son of Mahmoud Zahar, a senior Hamas official. Israel’s daily Ma’ariv quoted Israeli security officials as saying they were concerned Zahar could retaliate by intervening to prevent the release of Shalit.