JERUSALEM — Beyond sparking Israel’s first large-scale invasion of the Gaza Strip since last summer’s pullout, the Palestinian attack on an Israeli army outpost near the Gaza border and the kidnapping of a soldier raises serious questions about Israel’s security and foreign policies.

Right-wing politicians argue that Sunday’s attack, coupled with months of incessant rocket fire from Gaza on Israeli civilians, shows that the army has lost its deterrent capacity.

Ehud Olmert’s plan for a major unilateral withdrawal from the West Bank also is under fire, with some pundits maintaining that the latest turn of events will further erode public confidence in the prime minister’s pullback strategy.

Sunday’s attack left two Israeli soldiers dead and seven wounded. One soldier, Cpl. Gilad Shalit, was kidnapped by the militants and brought back to Gaza.

On Wednesday, Israeli soldiers and tanks punched back into the coastal strip, searching for Shalit. The “Summer Rain” operation was launched after two days of failed mediation over Shalit’s release.

“We won’t hesitate to carry out extreme action to bring Gilad back to his family,” Olmert said.

The attack that resulted in Shalit’s capture highlighted sharp differences on the Palestinian side. It came just days before Palestinian factions reached agreement on a document meant to pave the way for negotiations with Israel and was widely seen as an attempt to torpedo the deal. It also raised questions about the limits of power of both Palestinian Authority President Mahmoud Abbas and Prime Minister Ismail Haniyeh.

With many splinter militia factions acting independently or taking orders from Hamas’ more radical leadership abroad, it raised another fundamental question: Does any Palestinian leader have enough domestic clout to deliver on a deal with Israel?

Though there had been prior intelligence warnings, the Palestinian gunmen surprised the Israelis early Sunday by attacking from the Israeli side and not the Gaza side of the outpost. Eight Palestinian militiamen infiltrated through a recently dug 300-yard-long tunnel, coming out well inside Israeli territory.

They then turned back toward the border, firing at the Israelis who were facing Gaza. Two attackers were killed while the others made it back to Gaza, taking Shalit with them.

In return for information on Shalit, the abductors insisted on the release of all Palestinian prisoners under age 18 and all Palestinian women prisoners in Israeli jails.

The Palestinian leadership was divided. Abbas, who leads the Fatah movement, ordered a search for the soldier to hand him back to Israel.

Haniyeh, of Hamas, also favored a speedy resolution of the crisis. Both realized they had been presented with a chance to win diplomatic points and alleviate international sanctions against the Hamas led-government.

Danny Rubinstein, Arab affairs analyst for the Ha’aretz newspaper, called it “Haniyeh’s moment,” and suggested that he could make enormous international gains by forcing the militias to release the soldier.

But Haniyeh may not be calling the shots: According to Israeli sources, Khaled Meshaal, Hamas’ Damascus-based leader, is in control, ordering the militiamen to stick to their demand for a prisoner exchange.

Meshaal is strongly opposed to the agreement reached Tuesday between Abbas and Haniyeh on a document that gives Abbas a mandate to negotiate with Israel and calls for restricting terrorist attacks to areas Israel conquered in 1967.

In addition to the ground invasion, Olmert warned that Israel would target leaders behind terrorism, “wherever they were.” This was seen as a direct threat to Meshaal and Haniyeh.

“This is the essence of the government’s warning: The blood of Corporal Gilad Shalit is on all your heads, from Prime Minister Ismail Haniyeh down. There won’t be a Hamas government in Gaza or Ramallah, and many of its ministers won’t be alive, if they don’t return the Israeli soldier the way he left: on his feet,” analyst Ben Caspit wrote in Ma’ariv.

When Israel withdrew from the Gaza Strip last summer, it evolved a new military doctrine based on deterrence rather than occupation.

The thinking was that with the occupation of Gaza finished, Israel would have international backing to respond with overwhelming force to any attack on sovereign Israeli territory. So far, however, this has failed to create a deterrent balance.

For months Palestinians have been firing Kassam rockets at the town of Sderot. When Israeli retaliatory shelling has killed Palestinian civilians, the international outcry has been resounding.

Right-wing politicians now are pressing the government to launch a large-scale attack on Gaza to restore the army’s deterrence.

“We should send the following message to the Palestinians: ‘If you go on doing what you are doing, we will inflict such damage on you that it won’t be worth your while,’ ” Effie Eitam, a former brigadier general and legislator from the right-wing National Union-National Religious Party bloc, told JTA.

The persistent Palestinian attacks also are undermining Israeli public support for a unilateral pullback from the West Bank.

“The demographic threat at the root of the plan sounds frightening, but it is still distant and not palpable. The Kassam and the Hamas are nearby and obvious to everyone,” political commentator Aluf Benn wrote in Ha’aretz.

Where is all this heading — toward escalation and a total breakdown of order on the Palestinian side? Is it the final jockeying for position by Palestinian factions before they accept a cease-fire? Or will there be a familiar, two-pronged Palestinian policy, with moderates negotiating with Israel while radicals attack it?

Olmert still sees unilateral withdrawal as the best answer to all these unsavory scenarios — but decision time on both sides of the border seems to be rapidly approaching.