Lieutenant Colonel Richard Hecht, the international spokesperson for the IDF, told Sky News that Israeli troops have managed to regain control of some areas of southern Israel from militants.

"There are two last pockets of fighting," he said. "We have more or less stabilised control in all communities around Gaza."

Earlier, the IDF said fighting was occurring in as many as eight locations inside Israel.

More than 1,000 Palestinian targets hit - follow live updates

It said it thought the situation would be in "a better place", more than 48 hours since the beginning of the surprise attack.

Lieutenant Colonel Hecht said he was unsure if more Hamas fighters had come across the Gaza border.

"There could be a potential for more to come through. We are still looking at other options for them to infiltrate into Israel. We can't deny that," he said.

"We are trying to make sure our border is secure on the ground and in the sea."

Other key developments include:
• Hundreds of Israelis are being held hostage by Hamas, including women, children and the elderly;
• Israeli civilians have been gunned down in towns, along roads and at a techno music festival being held in the desert near Gaza;
• Central Israel has been targeted by a "huge rocket barrage";
• Israel's defence minister orders "complete siege" of Gaza Strip;
• Rishi Sunak to chair a COBRA emergency response meeting;
• More than 123,000 people have been displaced in Gaza, UN says.

Israel-Hamas War - watch special programme on Sky News tonight at 9pm.

Israeli forces moved to crush fighters still in southern towns and intensified their bombardment of the Gaza Strip with the number of dead reaching 1,100 and thousands wounded on both sides.

At least 700 people have reportedly been killed in Israel and 493 have died in Gaza as Israel retaliated with airstrikes in an operation which has been dubbed "Swords of Iron".

'Complete siege' of Gaza Strip

Israel's defence minister has ordered a "complete siege" of the Gaza Strip, saying authorities will cut electricity and block the entry of food and fuel.

Yoav Gallant said his country was "battling beastly people" and was conducting itself as such.

Around 300,000 reservists have been called up by the Israeli military.

Meanwhile, emergency services in Israel have said a "huge rocket barrage" had begun.

It is not yet clear where the rockets have been fired from, although Israeli media has speculated they are coming from the Gaza Strip.

Inside the Gaza Strip, more than 1,000 targets had been hit, the IDF said earlier, including airstrikes that levelled much of the town of Beit Hanoun in the northeast corner.

Around 159 housing units had been destroyed across the city and 1,210 others were severely damaged, according to the United Nations Office for the Coordination of Humanitarian Affairs.

On Monday, an Israeli air strike killed 19 people, including women and children, said Talat Barhoum, a doctor at the local Al Najjar Hospital in Gaza.

Four Israeli captives and their Hamas captors have been killed in strikes since Sunday, Hamas' armed wing said.

'Darkest day in our history'

The Israeli rescue service Zaka said its paramedics removed about 260 bodies from a music festival attended by thousands that came under attack.

The total number of dead is expected to be higher as other paramedic teams were working in the area.

Video on social media and Israeli news outlets showed dozens of festival-goers running through an open field as gunshots rang out. Many hid in nearby fruit orchards or were gunned down as they fled.

"It's the darkest day in our history," Lieutenant Colonel Jonathan Conricus, spokesperson for the IDF, said.

"You could say it's 9/11 and Pearl Harbor together for us," he told Fox News.

The declaration of war foreshadows heavier fighting ahead, and a major question is whether Israel will launch a ground assault into Gaza, a move that in the past has brought increased casualties.

During their rampage through southern Israel, militants dragged back into Gaza dozens of captives.

Authorities are still trying to determine how many civilians and soldiers were seized by Hamas fighters and taken back to Gaza.

From videos and witnesses, the captives are known to include women, children and the elderly.

Senior Hamas official Mousa Abu Marzouk told Arabic language news outlet al Ghad on Sunday that they were holding more than 100 people captive.

He said they would not be released until all Palestinian prisoners in Israeli jails are freed.

Read more:
Haunting messages left by Israelis taken hostage
What is Hamas - and why has it chosen now to strike?
British man serving in Israeli army killed in Hamas attack

At the UN, the United States called on all 15 members of the security council to strongly condemn "heinous terrorist attacks committed by Hamas".

How Hamas carried out deadly Israel attack

Meanwhile, Prime Minister Rishi Sunak will chair a COBRA emergency response committee meeting to discuss the situation in Israel, later today.

"We already have a very long-standing relationship with Israel, we are one of their strongest allies, we've provided in the past the kinds of equipment that they've used to defend themselves over the past couple of days," Mr Sunak told reporters in Nottinghamshire.

"And as I said to the prime minister (Benjamin Netanyahu), we will continue to provide, whether that's diplomatic, intelligence or security support as they need."