Olmert and the country's top security officials fear that unchecked settler violence could spark a new Palestinian intifada, enrage the Muslim world and compromise Israel's international standing.
They are also worried about a potential spillover into Israel proper, where extremist settlers could target prominent left-wingers or even national leaders. A little more than two months ago, a prominent left-wing professor and Israel Prize winner, professor Zeev Sternhell, was wounded by a pipe bomb planted outside his home.
The latest settler rampage came last week after Israeli police evacuated settlers from a building in Hebron. Jewish settlers had moved into the building in March 2007 after an American Jewish businessman claimed to have bought it for them, but the Palestinian owner denied selling it.
Israel's Supreme Court ruled last month that the building should be evacuated until the ownership issue was decided. On Dec. 4, in a well-planned operation, special police forces surprised the estimated 200 inhabitants, dragging them out in less than an hour.
The eviction triggered a paroxysm of settler violence against Palestinians in nearby neighborhoods. Settlers set fire to courtyards and olive trees, stoned vehicles and passers-by and terrorized Palestinian residents. In one case, a settler was filmed firing live ammunition from close range and wounding at least two Palestinian men. Settlers also destroyed headstones in a Muslim cemetery and spray-painted slurs on mosque walls.
Meanwhile, in front of the disputed Hebron building, they recited prayers against the government, the army and the police.
In a Cabinet meeting Sunday, Olmert did not mince words.
"The sight of Jews firing at innocent Palestinians has no other name than a 'pogrom,'" he declared. "I am ashamed that Jews could do such a thing. I have asked the defense minister and other relevant individuals to do all it takes and to use whatever force they need in any place under Israeli control to stop these outrages."
The violent settler response to the evacuation of the building, dubbed the House of Contention by Israeli media and called the Peace House by settlers, was symptomatic of a relatively new phenomenon: growing numbers of radical settlers who feel alienated from the state, don't accept its authority and are ready to use violence to prevent it from taking action against settler interests.
The eruption of violence in Hebron was not a case of spontaneous anger but part of a calculated strategy radical settlers call "price tag." The policy is intended to demonstrate to Israel that it will have to pay a very high price for any action the government takes against them in the hope that Israel eventually will get the message and desist.
This way, the settlers believe, they will prevent the Jewish settlements in the West Bank from suffering the same fate as those in the Gaza Strip, which were evacuated, destroyed and handed over to the Palestinians in the summer of 2005.
Two seminal events inform this radical thinking: the 2005 "disengagement" and the destruction of illegal settler homes at the West Bank outpost of Amona in February 2006.
Radical elements among the settlers attribute these setbacks to insufficient settler resistance to the government, hence the new price tag policy.
Radical settlers also are telling their followers that in working against the settler movement, successive Israeli governments have acted against Jewish principles, tikkun olam (repairing the world) and the messianic era, and therefore are illegitimate. Some settlers consequently have disavowed their allegiance to the State of Israel, refusing to serve in the army and backing the establishment of a rival breakaway Kingdom of Judea based on Torah and Jewish law.
The extremist fringe is estimated at between several hundred to a few thousand out of the West Bank's 300,000 settlers. Most of the settlers' leadership, including the Judea and Samaria Council, disavow the radicals. Dani Dayan, the council chairman, said they are doing the settler enterprise more harm than good. Others, however, have spoken out in defense of the radical settler youth.
This year has seen approximately 700 cases of settler violence against Palestinians and Israeli soldiers. More than 500 criminal complaints have been filed, and more than 200 people have been arrested.
The Shin Bet internal security service, which monitors radical Jewish activities on the West Bank, warns that extremists are ready to use live fire to stop peacemaking with the Palestinians.
There is deep concern that this sort of settler action could spark a new Palestinian intifada. Palestinian leaders have warned that if settler violence continues, acts of revenge are almost a certainty. This could spiral out of control quickly.
Some fear that if the Israeli army becomes involved against Palestinian lawbreakers, Palestinian police -- who have won kudos from Israel recently for the way they are keeping the peace -- might turn their weapons on the Israeli forces, sinking the peacekeeping framework their U.S. sponsors have so assiduously helped to build.
There is fear, too, that footage of Jewish graffiti on mosques and desecration of Muslim cemeteries will ignite the Muslim world the way the Mohammed caricatures in the Danish press did in 2005.
Already the settler violence has sparked severe European criticism of the radicals and of Israel's inability to contain them. If not addressed, it could severely undermine Israel's international standing.
As for the spillover of violence into Israel proper, the September attack outside Sternhell's home in Jerusalem almost certainly was perpetrated by radical right-wingers. Pamphlets at the site of the bombing referred to the Kingdom of Judea and offered a $275,000 reward to anyone who kills a dovish leader.
After the evacuation of the house in Hebron, radical settlers blocked roads into Israel proper. On Monday, small groups of settlers demonstrated outside the homes of the commander of the Israeli army's Judea and Samaria Division, the deputy state attorney and the head of the Shin Bet's Jewish desk, broadcasting a threatening message.
"In the same way as we were surprised in Hebron, we can surprise the law enforcers and get to their homes," they warned.
Olmert and Defense Minister Ehud Barak are taking the threat posed by the radicals very seriously.
The army has been given instructions to clamp down strongly on any hint of violence, and the Shin Bet's Jewish desk is stepping up its already intensive monitoring of radical groups.
Although the radicals have nothing like the wide base of tacit support they had when Yitzhak Rabin was assassinated by a right-wing extremist in 1995, the lesson of the past few months is that without concerted action by Israel's forces of law and order, these radical settlers will be very difficult to stop.