Israel kept up its deadly bombardment of Hamas-controlled Gaza Tuesday after the Palestinian militant group threatened to execute some of the around 150 hostages it abducted in a weekend assault if air strikes continue without warning.

Israel already imposed a total siege on the Gaza Strip on Monday, cutting off food, water and electricity supplies, and sparking fears of that an already dire humanitarian situation will swiftly deteriorate.

Israel has been left reeling by Hamas's unprecedented ground, air and sea assault, likening it to the September 11, 2001 attacks on the United States.

The death toll rose to more than 900 in Israel, which has retaliated with a withering barrage of strikes on Gaza, raising the death toll there to 687.

The Israeli army said Tuesday it had "more or less restored control" over the Gaza border after Saturday's mass breach by Palestinian gunmen.

It said it had recovered the bodies of around 1,500 Hamas militants inside Israel, confirming the scale of Saturday's assault.

It said it had "nearly completed" evacuation of Israeli communities around the border.

Fireballs repeatedly lit up Gaza City before dawn on Tuesday as explosions sounded and sirens wailed.

Hamas said Monday that Israeli air strikes had killed four of its hostages.

It later said it could start killing them itself.

"Every targeting of our people without warning will be met with the execution of one of the civilian hostages," Hamas armed wing, the Ezzedine al-Qassam Brigades, said in a statement.

In a televised speech late Monday, Israeli Prime Minister Benjamin Netanyahu compared Hamas to the Islamic State group, also known as ISIS, and said Israel planned to deploy "unprecedented force".

"Hamas terrorists bound, burned and executed children. They are savages. Hamas is ISIS," Netanyahu said.

He also vowed to "strengthen other fronts in the north against Hezbollah", where militants and Israeli forces exchanged fire for a second day.

Hamas launched more rockets as far as Tel Aviv and Jerusalem, where missile defence systems fired and air raid sirens blared.

Israel said it had called up 300,000 army reservists for its "Swords of Iron" campaign..

Defence Minister Yoav Gallant said Israel would impose a "complete siege" on the long-blockaded enclave of 2.3 million people: "No electricity, no food, no water, no gas -- it's all closed." 

United Nations chief Antonio Guterres said he was "deeply distressed" by the siege announcement, and warned Gaza's already dire humanitarian situation will now "only deteriorate exponentially".

Palestinians in the coastal territory braced for what many feared will be a massive Israeli ground attack aiming to defeat Hamas and liberate the hostages.

- Lebanon border clash -

Middle East tensions have spiked as Israel's arch enemy Iran praised the Hamas attack, although Tehran denied any direct role in the military operation.

Hamas has called on "resistance fighters" in the West Bank and in Arab and Islamic nations to join what it has dubbed "Operation Al-Aqsa Flood".

"The military operation is still continuing," Hossam Badran, a Hamas official, told AFP from Doha, adding that "there is currently no chance for negotiation on the issue of prisoners or anything else".

Israel, which has long prided itself on a high-tech military and intelligence edge, has been shaken to the core by the surprise Hamas strike, and now faces the threat of a multi-front war.

On Monday, the Israeli army said its soldiers had "killed a number of armed suspects" who had crossed the border from Lebanon and that Israeli helicopters were striking targets in the area.

The Palestinian militant group Islamic Jihad later claimed responsibility for the thwarted infiltration from Lebanon to Israel.

Iran-backed Hezbollah said Israeli strikes on south Lebanon killed three of its members, prompting the movement to retaliate against two Israeli barracks "using guided missiles and mortar shells that hit them directly".

It was the second day of an exchange of fire between Israel and Hezbollah, which on Sunday said its strikes were "in solidarity" with the Hamas attacks.

"We are deeply concerned about Hezbollah making the wrong decision and choosing to open a second front to this conflict," a senior US defence official said.

Washington, which moved its biggest aircraft carrier and other warships closer to Israel in a show of support, has said it has no plans to put US boots on the ground but is working with its ally on hostage recovery efforts.

 - 'Unbearable' -

Hamas's attack penetrated the Gaza border fence -- long deemed impregnable and guarded by surveillance cameras, drones, patrols and watchtowers.

More than 270 bodies, mostly young people, were strewn across the site of a music festival in a Negev desert kibbutz, while other revellers were feared to be among the captives taken into Gaza.

Israeli soldier Ephraim Mordechayev told AFP he witnessed Hamas attackers firing RPG missiles into the crowd.

"Imagine yourself using a rocket that is meant to fire on houses or tanks, fired on a group of 20 civilians," he said.

Inside Gaza, air strikes wrought widespread destruction in the Jabalia refugee camp, where charred bodies were pulled from the rubble and relatives wailed in grief.

Three Palestinians journalists have been killed in the fighting, the Committee to Protect Journalists said on Monday, with two photographers also reported missing since Saturday. 

Israel has blockaded Gaza since Hamas took control in 2007, leading to four previous wars with Israel.

Israeli strikes have levelled residential tower blocks, a large mosque and the territory's main bank building.

The UN Relief and Works Agency for Palestine Refugees said it was sheltering more than 137,000 people in schools across Gaza.

"The situation is unbearable," Amal al-Sarsawi, 37, said from a classroom with her terrified pupils.

In the West Bank, protesting Palestinians clashed with Israeli forces, leaving 15 Palestinians dead since Saturday.

- Global shock waves -

The spiralling conflict has been felt globally, with oil prices surging on fears of tightening supplies.

US energy firm Chevron said it suspended operations at a natural gas platform off Israel's coast at the request of authorities.

Saudi Arabia's de facto ruler Crown Prince Mohammed bin Salman told Palestinian president Mahmud Abbas in a phone call that the Gulf kingdom was working to prevent the conflict spreading across the region, state media said early Tuesday.

The European Commission said it was reviewing its development aid to the Palestinians, but clarified that no support had yet been suspended. Britain said it was undertaking a similar review.

The United States and European Union consider Hamas a terrorist group.

Analysts said the unprecedented nature of the Hamas assault could make any diplomatic efforts fruitless for now.

Turkish President Recep Tayyip Erdogan is among those trying, nonetheless. He held an urgent round of telephone diplomacy Monday.

Erdogan warned Israel against "indiscriminately" attacking civilians and also delivered measured criticism of Hamas, urging both sides to respect the "ethics" of war.

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