An exchange of fire between Israeli troops and "Palestinian terrorists" killed three of the militants in the southern Israeli city of Ashkelon, the Israeli army said.
Troops backed by helicopters and drones exchanged fire with "several terrorists in the industrial zone of Ashkelon," several kilometres north of Gaza the army said, continuing to search for holdout fighters of the Hamas militant group who carried out an unprecedented attack on southern Israel on Saturday.
US President Joe Biden has described the attack on Israel as "an act of sheer evil" and stressed US support for Israel as it mourned the killing of more than 1,000 people including 14 Americans.
"There are moments in this life, and I mean this literally, when the pure unadulterated evil is unleashed on this world.
"The people of Israel lived through one such moment this weekend," Mr Biden told reporters at the White House.
Mr Biden said American citizens were being held hostage by Hamas and that he had directed his team to share intelligence to help with hostage recovery efforts.
He said he was ready to order extra military forces to the Middle East in the wake of the attack.
He added: "The United States has also enhanced our military force posture in the region to strengthen our deterrence. "We stand ready to move in additional assets as needed."
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National security adviser Jake Sullivan told reporters at a separate briefing that the US believed 20 Americans were missing in the conflict.
He said: "We believe that there are 20 or more Americans who at this point are missing, but I want to underscore and stress that does not mean necessarily that there are 20 or more American hostages.
"Just that is the number who are currently unaccounted for."
US Secretary of State Antony Blinken plans to arrive in Israel on Thursday to meet with senior Israeli leaders, a US State Department spokesman told reporters.
Israel has continued to pound Gaza with the fiercest air strikes in its 75-year conflict with the Palestinians, razing whole districts to dust despite a threat from Hamas militants to execute a captive for each home hit.
Across the barrier wall surrounding Gaza, Israeli soldiers were collecting the last of the dead four days after Hamas gunmen rampaged through towns in by far the deadliest attack in Israel's history.
Israel's embassy in Washington said the death toll from Hamas' weekend attacks had surpassed 1,000, dwarfing all modern Islamist attacks bar 9/11.
Israel has vowed to take "mighty revenge", calling up hundreds of thousands of reservists and placing Gaza, crowded home to 2.3 million people, under total siege.
The victims were overwhelmingly civilians, gunned down in homes, on streets or at a dance party.
Scores of Israelis and some foreigners were captured and taken to Gaza as hostages, some paraded through the streets.
Gaza's health ministry said Israel's retaliatory strikes had killed at least 850 people and wounded more than 4,250.
The airstrikes, already the heaviest ever, intensified this evening, shaking the ground and pouring columns of smoke and flames into the morning sky.
Meanwhile, Russian President Vladimir Putin has said the explosion of violence showed the failure of US policy in the Middle East.
Mr Putin said the Kremlin was in touch with both the warring sides and that Moscow would seek to play a role in resolving the conflict but did not specify how.
Instead, Mr Putin took the opportunity to blame the sharp escalation on years of US policy in the region.
"I think that many people will agree with me that this is a vivid example of the failure of United States policy in the Middle East," Mr Putin told visiting Iraqi Prime Minister Mohammed Shia Al-Sudani.
Earlier, the United Nations said more than 180,000 Gazans have been made homeless, many huddling on streets or in schools.
At the morgue in Gaza's Khan Younis hospital, bodies were laid on the ground on stretchers with names written on their bellies.
Medics called for relatives to pick up bodies quickly because there was no more space for the dead.
A municipal building was hit while being used as an emergency shelter; survivors there spoke of many dead.
"There is an extraordinary number of martyrs, people are still under the rubble, some friends are either martyrs or wounded," said Ala Abu Tair, 35, who had sought shelter there with his family after fleeing Abassan Al-Kabira near the border.
"No place is safe in Gaza, as you see they hit everywhere," he said.
Radwan Abu al-Kass, a boxing instructor and father of three, said he had been one of the last to evacuate his five-storey building in the Al Rimal district after the area came under attack.
He finally left when a missile hit the building, which was destroyed by a bigger strike after he got out. "The whole district was just erased," he said.
Two members of Hamas' political office, Jawad Abu Shammala and Zakaria Abu Maamar, were killed in an air strike in Khan Younis in southern Gaza, a Hamas official said.
The Israeli military said they had been struck overnight. They were the first senior Hamas members killed since Israel began pounding the enclave.
Israel said Abu Shammala had led a number of operations targeting Israeli civilians. He was a member of the Hamas politburo in charge of economic affairs.
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Three Gaza journalists were killed when an Israeli missile hit a building while they were outside reporting, bringing the number of journalists killed to six.
UN High Commissioner for Human Rights Volker Turk, who denounced the Hamas attacks, said civilians had been harmed in Israeli strikes on tower blocks, schools and UN buildings.
"International humanitarian law is clear: the obligation to take constant care to spare the civilian population and civilian objects remains applicable throughout the attacks," he said.
In Israel, there has still been no complete official count of the dead and missing from Saturday's attacks.
In the southern town of Be'eri, where more than 100 bodies have been retrieved, volunteers in yellow vests and face masks solemnly carried the dead out of homes on stretchers.
A long, wide trail of blood wound along the floor of a house where bodies had been dragged out to the street from a blood-soaked kitchen strewn with overturned furniture.
"The thing I want the most is to wake up from this nightmare," said Elad Hakim, a survivor from a music festival where Hamas had killed 260 partygoers at dawn.
Arab cities have seen street demonstrations in support of the Palestinians. Iran, Hamas's patron, celebrated the attacks but denied playing a direct role in them.
Supreme Leader Ali Khamenei said that Iran kissed the hands of the planners of the attacks, but that anyone who believed Iran was behind them was mistaken.
The attacks had delivered a military and intelligence defeat to Israel that was beyond repair, he said.
A deadly clash on Israel's northern border yesterday raised fears of a second front in the war, with Iran's other main ally in the area, Lebanon's Hezbollah movement, being drawn into the fray. It said it was not behind any incursion into Israel.
The US' top general warned Iran not to get involved: "We want to send a pretty strong message.
"We do not want this to broaden and the idea is for Iran to get that message loud and clear," General Charles Q Brown, the chairman of the Joint Chiefs of Staff, told reporters travelling with him to Brussels.
Elsewhere, a salvo of rockets was fired from southern Lebanon towards Israel, three security sources told Reuters, in the third consecutive day of violence along the Lebanese-Israeli border.
One security source said the bombardment was carried out by Palestinian factions.
A second source said Israeli shelling was hitting the southern area from which the rockets were launched.
The Israeli military said it was responding with artillery fire to launches coming from Lebanese territory.
It said some 15 rockets were launched from Lebanon, of which four were intercepted and ten fell in open spaces.
Elsewhere, Tánaiste and Minster for Foreign Affairs Micheál Martin has said that Ireland will be "very clear" that EU humanitarian aid must continue to reach Palestine at a meeting later today.
Speaking to RTÉ News, he said that he has been through the first stage of a special meeting with EU foreign ministers today, and that "there is horror in respect of the scale of the atrocities committed against Israel and Israeli civilians following the attacks by Hamas".
He said there is concern about the evolving situation on the ground in Gaza in respect of Palestinians, families and children.
Mr Martin said: "The move by Israel to engage with Hamas and to deal with Hamas, that obviously will have consequences on the humanitarian side, and our contribution later will be very clear that humanitarian aid from the European Union has to continue to reach Palestinians in the area if education, in the area of health, and in the area of food provision."
He added that there is "real concern about the capacity of this situation to escalate wider across the region," and every effort should be made to ensure this does not happen.
