Palestinian militant group Hamas, which dragged off about 150 hostages in its surprise weekend assault on southern Israel, threatened on Monday to kill them if Israeli air strikes continue "targeting" Gaza residents without warning.

The threat came after Israel imposed a total siege on the Gaza Strip, cutting off the water supply which sparked UN fears of an increasingly dire humanitarian situation.

Israel continued bombing targets in response to the surprise Hamas assault it has likened to the 9/11 attacks.

Reeling from the Palestinian Islamist group's unprecedented ground, air and sea attacks, Israel has counted 800 dead and launched a withering barrage of strikes on Gaza that have raised the death toll there to 560.

Fireballs repeatedly lit up the darkness of Gaza City Monday night as explosions sounded and sirens wailed.

Hamas — whose militants surged into Israeli towns on Saturday, spraying gunfire at civilians and dragging off captives — claimed on Monday that Israeli air strikes had killed four of the 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," the Ezzedine al-Qassam Brigades, the armed wing of Hamas, said in a statement.

Israeli Prime Minister Benjamin Netanyahu earlier threatened that "what Hamas will experience will be difficult and terrible … We are going to change the Middle East.

"This is only the beginning," he vowed. "We will defeat them with force, enormous force."

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, and truck convoys were moving tanks to the south, where its forces were working to dislodge holdout Hamas fighters from embattled towns.

Libby Weiss, an Israeli military spokeswoman, said some Hamas militants "are still there right now", after about 1,000 militants had penetrated the region on the Jewish Sabbath.

Defence Minister Yoav Gallant said Israel would impose a "complete siege" on the long-blockaded enclave and stressed what this meant for its 2.3 million people: "No electricity, no food, no water, no gas — it's all closed."

United Nations Secretary-General Antonio Guterres warned this will compound Gaza's already dire humanitarian situation.

"Now it will only deteriorate exponentially," he said.

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 and their Lebanese ally Hezbollah praised the Hamas attack, although Tehran rejected any direct role in the military operation.

Hamas has called on "resistance fighters" in the occupied West Bank and in Arab and Islamic nations to join its "Operation Al-Aqsa Flood", launched half a century after the 1973 Arab-Israeli war.

"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".

The United States has pledged "rock solid" support for Israel and said it would send munitions and military hardware to its key ally and divert an aircraft carrier group to the eastern Mediterranean, amid fears of a wider conflagration.

Israel, which has long prided itself on a high-tech military and intelligence edge in its many conflicts, has been shaken to the core by Hamas's unprecedented attack.

It now faces the threat of a multi-front war after Hezbollah launched guided missiles and artillery shells from the north on Sunday "in solidarity".

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.

Hezbollah said an Israeli strike on a south Lebanon watchtower killed three of its members.

'They butchered people' 

Israel has expressed alarm and revulsion at the Hamas attack across the Gaza border fence — long deemed impregnable and guarded by surveillance cameras, drones, patrols and watchtowers.

Among the hostages they took back into Gaza were children and a Holocaust survivor in a wheelchair, Israeli officials have said.

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 hostages.

"They butchered people in cold blood in an inconceivable way," said Moti Bukjin of the Zaka religious volunteer group which helped collect the human remains.

Israelis have voiced anger at the intelligence failure.

But for now its people appear to have put aside divisions that this year split the country, and even its military, and braced for what the right-wing veteran premier Netanyahu warned will be a "long and difficult war".

'In constant fear' 

"Never before have so many Israelis been killed by one single thing, let alone enemy activity in one day," said army spokesman Jonathan Conricus.

The multi-pronged attack had brought "by far the worst day in Israeli history", he said, likening it to a combination of the "9/11 and Pearl Harbour" attacks.

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.

Israel has blockaded Gaza since Hamas assumed control there in 2007, leading to four wars with Israel before the latest escalation.

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

More than 120,000 people in Gaza have been displaced, said the United Nations.

"The situation is unbearable," said Amal al-Sarsawi, 37, sheltering in a school classroom with her terrified children.

Global shock waves 

Palestinians in the West Bank have rallied in support and clashed with Israeli security forces, leaving 15 Palestinians dead since Saturday.

Mourners in Hebron waved green Hamas flags during the funeral procession for one of them, Muhammed Jawad Zughayer, 21.

In Rafah, Gaza, mourners buried six members of a family killed when an air strike hit their home.

Anti-Israel activists have demonstrated in many countries while security was stepped up around Jewish temples and schools worldwide.

The spiralling conflict has sent shock waves around the globe, sparking a surge in oil prices 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 there.

Western capitals condemned the attack by Hamas, which the United States and European Union consider a terrorist group.

The EU has halted development aid payments to the Palestinians and said it was placing 691 million euros of support "under review".

Foreign or dual nationals have been reported killed, abducted or missing by countries including Brazil, Britain, Cambodia, Canada, France, Germany, Ireland, Mexico, Nepal, Panama, Paraguay, Russia, Thailand, Ukraine and the United States.

The Arab League said its foreign ministers will hold an extraordinary meeting on Wednesday to discuss the "Israeli aggression".

The leaders of Britain, the US, France and Germany were also to hold talks later Monday. This "must not be allowed to become a conflagration in the region," said German Chancellor Olaf Scholz.