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Israeli forces say they are now in the heart of Khan Younis, the second largest city in the Gaza Strip and an area once-declared a safe zone.
Israeli government spokesman Eylon Levy says their troops continue to battle Hamas militants in Khan Younis.
"Our commando forces are conducting raids in Khan Younis and battling Hamas terrorists with forces striking targets using precise real time intelligence. In the north, we have also seen intense fighting between IDF forces and Hamas forces in Jabaliya and Shijaiya, which have been completely encircled. We have broken through their defensive lines, and those terrorists are now emerging from their underground tunnels to engage our men in close combat."
Gaza's Hamas-run health ministry says at least 350 Palestinians have been killed in the last 24 hours.
Shadi Abu Samra, who witnessed the airstrike, say dozens of people are feared to be buried beneath the rubble.
"There were people having breakfast, safely sitting, baking or filling water. There is no safety. There is no safe area. All the missiles are falling over people’s heads. God will judge everyone staying silent, every single person staying silent. More than 70 persons are trapped under us. We can’t pull them out. People, for God’s sake feel for us. More than 70 persons are (trapped) under here. They’re still pulling people. We pulled out from maybe more 20 or 30 persons, and they’re still at it. Right below our legs there are probably some 70 people."
Tens of thousands of Palestinians are fleeing to Rafah in southern Gaza in a desperate attempt to escape the Israeli airstrikes.
Moneer Al Nabrees is among the 1.87 million Palestinians displaced by the war.
He says he was told to come to Muwasi, a so-called safe zone and refugee settlement-turned-small-town in southern Gaza.
"We came here according to the army's call because the area is safe as they promised us. To be frank, the area had no services. Really Challenging. Tents were overcrowded with each one housing 30 to 40 people. We are suffering from the very cold weather and there are no necessities of life. There are queues for everything, even to get drinking water. We are suffering a lot because of this and the children are deeply depressed due to the situation. We are suffering like hundreds of thousands of our people."
Israel has blamed the high civilian death toll in Gaza on Hamas, accusing it of using civilians as human shields.
Senior Hamas official Osama Hamdan says as Israel's offensive intensifies, the possibility of returning further Israeli hostages decreases.
United States National Security spokesman John Kirby says it's unlikely Israel and Hamas will reach a new ceasefire agreement anytime soon.
"We're not close to inking another deal on a humanitarian pause. And nor do I have any news to break here today about the return of hostages, either ours or those of many other countries that are being held hostage. We're still trying to get as much information as we can about the hostages that are being held. We have some information, as I said before, on some of the hostages because their families are talking to us. And that's been a terrific source of information and context."
Meanwhile, hundreds of people have gathered in Tel Aviv to light the first candle of Hanukkah with families of hostages held by Hamas militants in the Gaza Strip.
Sixteen-year-old Amit Shanny, a released hostage, was among those who addressed the crowd.
"I am very excited to stand here tonight for the first candle of Hanukkah on the land of Israel. I want to thank everyone, to everyone who worked to return the hostages, and all those who returned. It makes me so happy to be here, with family and friends. We must continue the fight until the last hostage returns."
In other developments, arrangements are being made for Australia's Foreign Minister Penny Wong to visit the Middle East in the New Year.
Ahead of that visit, the government will send Assistant Foreign Minister Tim Watts alongside opposition spokesman Simon Birmingham to Israel next week.
A spokesperson for Foreign Affairs has said Australia's been working with countries that have "influence in the region" to help civilians, and to "reinforce the need for the just and enduring peace that all of us want."
Deputy Prime Minister Richard Marles says accordingly it is right for senior ministers to travel to the country.
"We maintain good relations with Israel as we do with a number of countries in that region and of course across the world. This is all itineraries which are worked out pretty close to when our travel occurs, but ultimately that's a matter for the Foreign Minister, but her travel is entirely appropriate."
