JERUSALEM — A 16-month cease-fire by several terrorist factions is faltering after members of a Palestinian family were killed in an explosion on a Gaza beach, providing the sternest test yet of the new security doctrine Israel forged after last year’s Gaza withdrawal.

The terrorist cease-fire was never absolute, and various Palestinian groups broke it when it suited them, citing a variety of grievances. But Hamas, which has refrained from attacks on Israel since it declared a truce early in 2005, now is threatening non-stop bombardment of the southern Israeli border town of Sderot — and a renewal of its suicide bombing campaign.

In response, Israel is considering a large-scale assault on the coastal strip, short of the introduction of ground forces. Defense Minister Amir Peretz has warned that Hamas leaders, no matter how high up in the Palestinian Authority hierarchy, will be targeted if they are seen to be promoting terrorism in any way.

In a meeting of top army brass Sunday, Peretz resisted calls for immediate action and decided to give the Palestinians two days “to get the message.” But there’s no indication that they have: Sderot, Peretz’s hometown, has been under constant fire by Palestinian Kassam rockets since Saturday.

Last Friday’s deaths on the Gaza beach also could put pressure on P.A. President Mahmoud Abbas to call off the referendum on a two-state solution with Israel that he set for late July.

The Hamas-led P.A. government has been strongly opposed to a referendum since the idea was discussed a month ago.

During the past few weeks, persistent Palestinian rocket attacks, and Israeli operations to stop them, have created a dangerous situation for civilians on both sides.

Tuesday saw an Israeli airstrike that killed Islamic Jihad’s main rocket launcher, Hamoud Wadiya, and at least one other Islamic Jihad member en route to a rocket attack. A rocket in the terrorists’ vehicle detonated by the strike and shrapnel from one of the Israeli missiles killed at least seven Palestinian bystanders.

Last Friday afternoon, Israeli aircraft, naval vessels and artillery fired on rocket-launching teams and areas they use as launching pads. Shortly afterward, an explosion on a Gaza beach killed nine Palestinians.

Initially it seemed likely that a stray Israeli artillery shell, one of six fired at the time, may have caused the carnage. But Israeli officials later said there was a discrepancy between the time the artillery round was fired and the time the Palestinians say the explosion on the beach occurred. They also noted that Hamas militiamen quickly removed all traces of the explosive device from the scene and denied Israel access to the evidence.

On Tuesday, Israeli investigators concluded that a Palestinian land mine, a Kassam rocket gone awry or an old, unexploded shell caused the damage. This was based partly on the absence of the large crater that would have been created by such an attack. Further, an analysis of shrapnel found in one of the Palestinian casualties found that the weapon was not Israeli-made.

Hamas dismissed the investigation as an Israeli attempt to avoid responsibility.

Israeli intelligence sources further claim that Hamas made a strategic decision to break the truce several days before the beach incident in order to create war-like conditions in which the planned Palestinian referendum couldn’t possibly go ahead.

Still, what actually happened on the beach is perhaps less important than how it is perceived. Palestinians accuse Israel of a deliberate massacre, and the image of 11-year-old Huda Ghaliya running distraught along the beach screaming for her dead father could become the icon that fuels a renewed Palestinian intifada.

The Hamas leadership abroad, under Khaled Meshaal, is pushing for an immediate end to the truce and a full-scale resumption of the terrorist war against Israel. The Hamas leadership in the territories, under P.A. Prime Minister Ismail Haniyeh, is more circumspect and opposes attacks inside Israel proper.

On the ground, however, Hamas militiamen have moved Kassam rockets into position in dozens of locations throughout Gaza. Palestinians fired 69 Kassams at Sderot over the weekend, severely wounding one man near a school and disrupting everyday life in the town.

There are different Israeli assessments over how long the Hamas offensive is likely to last. Alex Fishman, a military analyst for the Yediot Achronot newspaper, says the predominant view is that “Hamas will hit hard and as soon as it feels it has done enough, it will stop the shooting and resume its low profile, because the lull is, in the final analysis, in Hamas’ interest.”

Other analysts believe the attacks could go on indefinitely, first to torpedo Abbas’ planned referendum and then to undermine Israeli Prime Minister Ehud Olmert’s planned unilateral withdrawal from the West Bank. The assumption is that Israel will not want to withdraw under heavy Hamas attack, but that if it does, Hamas will be able to claim credit.

For Israel, the escalation is a test of its new security doctrine: After withdrawing from Gaza last year, Israel believed it had a free hand to retaliate to attacks with considerable force and hoped to create a balance of deterrence like the one with Hezbollah along the Lebanese border.

So far, despite the targeted killings of rocket-launch crews and the naval and artillery bombardments, Israel has not been able to create a deterrent. It remains to be seen whether the specter of a large-scale Israeli assault on militia and infrastructure targets in Gaza, coupled with the threat to assassinate political leaders who dabble in terrorism, will be more effective.

The killing on the beach also has sparked an internal Israeli debate on the ethics of conflict. Left-wing Israelis argue that continuing hostilities inevitably will claim innocent victims on both sides, and that the pressing need is to find a way to stop the violence. Right-wingers counter that Israel should not allow accidental civilian casualties on the Palestinian side to deflect it from defending its citizens.

The sharpest exchanges came in Ma’ariv’s daily newspaper, between left-wing novelist David Grossman and the paper’s editor, Amnon Dankner.

“The image of the girl on the Gaza beach, whose life was torn to shreds before our very eyes, should rouse us from the hypnotic coma we have been in for years,” Grossman wrote.

Israel, he wrote, should break the futile cycle of violence by declaring a unilateral cease-fire and calling for negotiations without preconditions.

Dankner disagreed vehemently.

“Given what we have been through, the notion that if only we would give peace a chance is so idiotic that the mind boggles in wonder when we hear this kind of thing,” he fumed. In his view, Israel “left Gaza to the last centimeter, in a painful, wrenching move. We destroyed settlements and families, and we have a right to demand absolute quiet from the Palestinians in the strip.”