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

The threat came after Israel on Monday imposed a total siege on the Gaza Strip, cutting off food, water and electricity supplies, and sparking fears of an increasingly dire humanitarian situation.

Israel has been left reeling from Hamas's unprecedented ground, air and sea attacks, likening them to 9/11.

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

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

Hamas -- which the Israeli army estimates sent about 1,000 fighters across the border, spraying gunfire at civilians -- said 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.

In a televised speech Monday night, Israeli Prime Minister Benjamin Netanyahu compared Hamas to the Islamic State group, also known as ISIS, and said Israel planned to carry out a "massive" assault against Hamas with "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. Truck convoys moved tanks to the south, where its forces were working to dislodge holdout Hamas fighters.

Israeli military spokeswoman Libby Weiss said some Hamas militants "are still there right now".

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 Secretary-General 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 rejected 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 has long prided itself on a high-tech military and intelligence edge in its many conflicts. But it has been shaken to the core by the 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.

 - 'They butchered people' -

Israel has expressed alarm and revulsion at Hamas's attack across 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.

"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.

Among the hostages were children and a Holocaust survivor in a wheelchair, Israeli officials have said, while foreign or dual nationals have been reported abducted or missing by countries including Thailand, Germany, Argentina, France and the United States.

Israelis have voiced anger at the intelligence failure. 

But for now, its people appear to have put aside divisions over plans by Netanyahu's hard-right government for judicial reforms.

In his speech, Netanyahu called on opposition leaders to immediately form "an emergency government of national unity without any preconditions".

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 previous wars with Israel.

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

- Global shock waves -

In the West Bank, Palestinians have rallied in support and clashed with Israeli 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, on Monday.

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

The spiralling conflict has been felt globally, with oil prices surging on fears of tightening supplies and demonstrations supporting both Israel and Palestine staged in many countries.

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

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

Around '1,500 bodies' of Hamas militants found in Israel: army 

Around 1,500 bodies of Hamas militants have been found in Israel around the Gaza Strip, the army said Tuesday, as it pummelled the Palestinian enclave with air strikes.

"Approximately 1,500 bodies of Hamas militants were found in Israel around the Gaza Strip," military spokesman Richard Hecht told reporters, adding that security forces had "more or less restored control over the border" with Gaza.

"Since last night we know that no one came in .. but infiltrations can still happen."

The army had "nearly completed" evacuation of all the communities around the border, he added.

Israel is reeling under a deadly attack by Hamas militants who stormed through the border fence under a barrage of rocket fire on Saturday morning and killed more than 900 people inside Israel.

In response Israel is carrying out a massive air and artillery bombardment of Hamas targets in the Gaza Strip that has so far killed at least 687 people in the coastal enclave.