Fighting between Israeli forces and Hamas Palestinian militants was ongoing Monday in seven to eight locations around the Gaza Strip inside Israel, the army said.
"We're still fighting. There are between seven to eight open places around Gaza (where) we have still warriors fighting terrorists," military spokesman Richard Hecht told reporters, two days after the Palestinian Islamist group launched a surprise attack on Israel.
"We thought by yesterday we would have full control. I hope we will by the end of the day."
During the night Israel carried out more than 500 air and artillery strikes targeting Hamas and Islamic Jihad militant groups in the coastal enclave as the death toll from its war with Palestinian militants surged above 1,100.
Prime Minister Benjamin Netanyahu had warned Israel to prepare for a "long and difficult" war after Palestinian militant group Hamas launched a surprise assault from Gaza on Saturday, firing a barrage of rockets and sending a wave of fighters who gunned down civilians and took at least 100 hostages.
More than 700 Israelis have been killed since Hamas launched its large-scale attack, the Israel Defence Forces (IDF) said on Monday. Another 1,200 people have been wounded, many critically.
In retaliation, Israeli air strikes have hammered the impoverished and blockaded Gaza Strip, an enclave of 2.3 million people, with officials there reporting at least 413 Palestinian deaths.
"Overnight IDF fighter jets, helicopters, aircraft and artillery struck over 500 Hamas and Islamic Jihad terrorist targets in the Gaza Strip," the military said in a statement.
Thick plumes of smoke billowed from the Palestinian enclave as the strikes continued in the early hours of the morning, an AFP correspondent reported.
'By far the worst day in Israeli history'
IDF spokesperson Lieutenant Colonel Jonathan Conricus estimated around 1,000 Palestinian militants had participated in Hamas's assault on Saturday, which he called "by far the worst day in Israeli history".
"Never before have so many Israelis been killed by one single thing, let alone enemy activity in one day," he said.
"This could be a 9/11 and a Pearl Harbour wrapped into one."
Around 100,000 reserve troops have been deployed to the south as the IDF battles to expel Hamas fighters from Israeli territory, he said, adding that a "very large amount" of Israeli civilians and soldiers were being held inside Gaza.
US President Joe Biden ordered "additional support for Israel in the face of this unprecedented terrorist assault by Hamas".
At least four US citizens were killed in the attack, US Senate Majority Leader Chuck Schumer said in a statement after a briefing, adding that the toll was likely to rise.
US Defence Secretary Lloyd Austin said Washington "will be rapidly providing the Israel Defense Forces with additional equipment and resources, including munitions".
Austin directed the USS Gerald R. Ford aircraft carrier and group of warships to the eastern Mediterranean and said that Washington was augmenting fighter aircraft squadrons in the region.
Hamas has said the US aid amounts to "aggression" against Palestinians.
- Abducted to Gaza -
Israel was stunned when Hamas launched its multi-pronged offensive on Saturday, the Jewish Sabbath, with at least 3,000 rockets raining down as fighters infiltrated towns and kibbutz communities and stormed an outdoor rave where many revellers were shot dead.
Panicked Israelis hiding in their homes told reporters that militants were going door to door and shooting civilians or dragging them away.
At least 100 citizens were captured by Hamas and abducted into Gaza, with images circulating on social media of bloodied hostages.
Yifat Zailer, 37, said she was horrified to see video footage from Gaza that showed her cousin and the woman's children, aged nine months and three years.
"That's the only confirmation we have," she told AFP, her voice breaking with emotion, and adding there was no information on her cousin's husband or her elderly parents.
"After the army took control of the kibbutz, they weren't at home," she said. "We assume they were kidnapped ... We want to know what their condition is, we want them to return safe. They're innocent civilians."
Israel also came under attack from the north when Lebanon's Hezbollah launched guided missiles and artillery shells Sunday "in solidarity" with the unprecedented Hamas offensive, without causing any casualties.
Israel responded with artillery strikes across the UN-patrolled border.
"We recommend Hezbollah not to come into this," said army spokesman Richard Hecht. "If they come, we are ready."
- 'Situation is unbearable' -
Netanyahu -- who leads a hard-right coalition government but has received pledges of support from political opponents -- has vowed to turn Hamas hideouts "to rubble" and urged Palestinians there to flee.
Israeli attacks since then have levelled several Gaza residential towers and destroyed a mosque in Gaza's Khan Yunis, as well as hitting the central bank.
More than 20,000 people in the Palestinian territory have been displaced due to fighting, the United Nations Relief and Works Agency for Palestine refugees (UNRWA) said.
From a classroom shelter in Gaza City, 37-year-old Amal Al-Sarsawi told AFP she had been awake all night comforting her terrified children.
"The situation is unbearable psychologically and economically," she said.
- Global impact -Western capitals have condemned the attack by Hamas, which Washington and Brussels consider a terrorist group.
The conflict has had global impact, with several other countries reporting nationals killed, abducted or missing, among them Brazil, Britain, France, Germany, Ireland, Mexico, Nepal, Thailand, Ukraine and the United States.
Oil prices soared more than four percent Monday, sparking concerns about possible supply shocks from the crude-rich region.
Israel's foes have praised the assault, including Iran whose President Ebrahim Raisi voiced support when he spoke with the leaders of Hamas and the Islamic Jihad group.
Pro-Palestinian demonstrations took place in the United States, Iraq, Pakistan and other countries, while Germany and France were among nations stepping up security around Jewish temples and schools.
In the Egyptian city of Alexandria a police officer opened fire "at random" on Israeli tourists Sunday, killing two of them and their Egyptian guide before he was arrested.
- Hamas calls for help -
Dubbing its attack "Operation Al-Aqsa Flood", Hamas called on "resistance fighters in the West Bank" and "Arab and Islamic nations" to join the battle.
Its attack comes half a century after the 1973 invasion by Egyptian and Syrian forces, a conflict known in Israel as the Yom Kippur War, and has sparked bitter recriminations for what was widely seen as an intelligence failure.
"There was a very bad failure here," said Sderot resident Yaakov Shoshani, 70. "The Yom Kippur War was small compared to it, and I was a soldier in the Yom Kippur War."
He recalled the terror in their town near Gaza.
"I held a kitchen knife and a large screwdriver, and I told my wife that, if something happens, to make sure to read the Kaddish (prayer) over me, if you stay alive," he said. "And so we stayed close to each other at home, shut everything and turned off the lights."
Hamas chief Ismail Haniyeh has predicted "victory" and vowed to press ahead with "the battle to liberate our land and our prisoners languishing in occupation prisons".
An Israeli survivor of the attack on Sderot, Yitzhak, 67, said he now expected the army to "conquer Gaza house by house, clean the area there properly, and not leave Gaza until they get the very last rocket out of the ground."
Many Gaza residents voiced defiance.
"We will not give up, and we are here to stay," said Mohammed Saq Allah, 23. "This is our land, and we will not abandon our land."