Israeli tanks and infantry have advanced on Gaza City from two directions, with tanks reported to be on the main north-south road, in an apparent effort to cut the strip into two. Reports in the Hebrew media, statements from Hamas and Palestinian witness accounts, described Israeli armour operating close to the Mediterranean coast in the north of Gaza in an area where Hamas said it was engaged in heavy fighting. Witnesses said Israeli tanks had advanced to cut the main north-south Salah al-Din road south of Gaza City and were operating on the outskirts of the Zaytun district and Shejaiya neighbourhood of Gaza City. Video taken by a local journalist was said to show an Israeli tank and bulldozer in central Gaza blocking the main highway and firing on a car, which was seen exploding. Meanwhile, Israel said it had rescued a female soldier kidnapped during Hamas’s 7 October massacre in southern Israel. The soldier was named as Ori Megidish, a private who serves as a border observer, who was rescued overnight on Monday in undisclosed circumstances. She was described as in good health following a reunion with her family. Megidish’s release came as Hamas released a video showing three female hostages appealing to be swapped for Palestinian prisoners in Israeli jails. The women were later identified in Israeli media as Elena Trupanov, Danielle Aloni and Rimon Kirsht, who had been kidnapped from border communities. Responding to the Hamas video, in which one of the hostages addresses an angry message to Benjamin Netanyahu, the Israeli prime minister condemned it as “cruel psychological propaganda”. Describing an increased tempo of urban fighting, the Israel Defence Forces spokesperson R Adm Daniel Hagari said Israeli troops were involved in fighting with armed Palestinian factions holed up in buildings. “Overnight, troops eliminated dozens of terrorists who barricaded themselves in the buildings and tried to attack the forces that were moving in their direction,” he said, adding that fighting was continuing. In one incident, the Israeli military said a fighter jet had targeted a building “with over 20 Hamas terrorist operatives inside”, while another fighter jet was guided to an anti-tank missile launching post in the area of al-Azhar University, it said. The university is in the heart of Gaza City. The military also said it had hit “weapons depots, dozens of anti-tank missile launching positions, as well as hideouts and staging grounds used by the Hamas terrorist organisation”. The escalating assault came amid increasing questions in Israel and among its international backers over what end game Israel envisaged for Gaza amid only vaguely articulated war aims. The UN and medical staff in Gaza warned that airstrikes had hit closer to hospitals where tens of thousands of Palestinians have sought shelter alongside thousands of wounded. In the heart of Gaza City itself, footage from Dar al-Shifa hospital showed people who had recently died laid on the ground in white shrouds. Some shrouds contained the dismembered remains of several people, Salama Maarouf, the head of the Hamas-run media office, told Al Jazeera. Dozens of the bodies could not be identified – in some cases because entire families had been killed – and were to be buried in a mass grave, he said. “We do not know their identity on this Earth, but they are known in the heavens,” he said. Aid agencies said the humanitarian crisis in Gaza continued to worsen, with insufficient water, food, medicine and fuel. On a visit on Sunday to Gaza’s Rafah border crossing with Egypt – the only entry point for a thin trickle of aid – the international criminal court’s top prosecutor, Karim Khan, said impeding aid could constitute a war crime and urged Israel to allow more trucks to enter. The Palestinian death toll in the Israel-Hamas war has reached 8,306, according to the Hamas-run health ministry in Gaza. In the occupied West Bank, more than 110 Palestinians have been killed in violence and Israeli raids. More than 1,400 people in Israel have been killed, most of them civilians who died in the Hamas rampage on 7 October. In addition, 240 hostages were taken from Israel into Gaza by the militant group. On Monday, the family of Shani Louk, a 22-year-old German Israeli initially believed to have been kidnapped alive during Hamas’s assault on a music festival in Re’im, said she was dead. “Unfortunately we got the news yesterday that my daughter is no longer alive,” her mother, Ricarda, told the German RTL/ntv station. Violence flared beyond Gaza. An Israeli jet struck what the IDF called a “military infrastructure” target in Syria. In Jerusalem, an assailant stabbed and seriously injured a police officer. Other officers had shot and arrested the assailant, said a police statement. The deepening IDF incursion into Gaza came amid dwindling Israeli public enthusiasm for a prolonged occupation. Support has fallen from 65% on 10 October to 46%, according to a study by the Hebrew University of Jerusalem, which has monitored the same sample of 1,774 people, with a 4.2% margin of error. “We see a continuation of the decline in Israeli support for occupying Gaza,” said Nimrod Nir, a researcher at the social science faculty. “The shock we saw in the first week, the rage we saw in the second, are slowly moderated and now Israelis care more about the hostage situation, are less inclined to enter a full-scale occupation.” Netanyahu appeared increasingly beleaguered after trying to deflect blame for the Hamas onslaught. On Sunday, he tweeted that his security chiefs had assured him Hamas was contained and had no plans to attack. Hours later he deleted the post and apologised. The debacle prompted criticism even from allies, who said Netanyahu had facilitated Hamas’s grip on Gaza as part of a strategy to divide Palestinians. “Since coming to power in 2009, Netanyahu has built up Hamas as an alternative to the Palestinian Authority,” wrote Yoav Limor, the military affairs correspondent for Israel Hayom, a normally pro-Netanyahu newspaper. “He was warned countless times that this was a dangerous plan: instead of bolstering the pragmatic elements, he strengthened those that will never recognise Israel’s existence.” Ben Caspit, a commentator in Ma’ariv, called Netanyahu a “scarecrow that is stuffed with rags playing the role of prime minister” and urged his party, Likud, to remove him. “He is unfit physically, he is unfit mentally, he is unfit morally. He needs to step down, and the sooner the better.” Asked at a news conference if he had considered stepping down over mounting public criticism of his leadership, Netanyahu said: “The only thing that I intend to have resigned is Hamas. We’re going to resign them to the dustbin of history. That’s my goal. That’s my responsibility.” Netanyahu added he would not agree to a ceasefire, saying it would be tantamount “to surrender to Hamas, to surrender to terrorism, to surrender to barbarism. That will not happen”.