Intense Israeli airstrikes have continued in Gaza after the prime minister, Benjamin Netanyahu, vowed to press Israel’s advance into the territory with “full force” and laid out an uncompromising vision of a postwar settlement. The bombardment on Sunday appeared concentrated around al-Shifa hospital in Gaza City, the biggest such facility in the territory, where much of the most intense fighting between Hamas and Israeli ground forces is taking place. The hospital was “totally surrounded and bombardments are going on nearby”, its director, Mohammad Abu Salmiya, said in a statement late on Saturday. The fierce clashes over recent days have trapped thousands of sick, wounded and displaced people in al-Shifa with no electricity and dwindling supplies. Medics and aid workers have warned patients will die unless there is a pause in the battle. Thousands more are trapped in other health facilities in the north of Gaza as Israel’s campaign to “crush” Hamas moves towards its sixth week. Despite growing pressure from even staunch allies, Netanyahu has so far rejected international calls for a ceasefire. “The war against [Hamas] is advancing with full force, and it has one goal: to win. There is no alternative to victory,” he said late on Saturday in televised comments. Netanyahu also made clear he wanted Israel to retain overall security control after any conflict “with the ability to go in whenever we want in order to kill terrorists”. “There will be no Hamas. There will be no civilian authority that educates their children to hate Israel, to kill Israelis, to destroy the state of Israel. There can’t be an authority there that pays the families of murderers. There needs to be something else there,” he said. The comments appeared to rule out any role for the Palestinian Authority after the conflict, a solution favoured by the US and many European powers. Israel has said doctors, patients and thousands of evacuees who have taken refuge at hospitals in northern Gaza must leave so it can tackle Hamas gunmen who, it says, have placed command centres under and around them. Hamas denies using hospitals this way. Medical staff say patients could die if they are moved and Palestinian officials say Israeli fire makes it dangerous for others to leave. Israel believes that Hamas has its headquarters beneath al-Shifa, claims which the hospital and Hamas have denied. “The medical team cannot work and the bodies, in their dozens, cannot be managed or buried,” said Abu Salmiya. Two newborns had already died on Saturday after the hospital’s fuel ran out and dozens more were at risk, officials said. The Israeli military described fierce close-quarter fighting in the area but denied any “siege” of al-Shifa. Israeli forces had observed “temporary tactical pauses” and opened “humanitarian corridors” to allow those trapped by the fighting to flee to relatively safer zones to the south, they said. An Israeli military statement on Sunday said soldiers had “opened and secured a passage which enables the civilian population to evacuate, on foot and by ambulances, from the Shifa, Rantisi and Nasser hospitals”. The World Health Organization expressed “grave concern” for the safety of everyone trapped in al-Shifa by the fighting and said it had lost communications with its contacts there. “As horrifying reports of the hospital facing repeated attacks continue to emerge, we assume our contacts joined tens of thousands of displaced people and are fleeing the area,” the organisation said on X, formerly Twitter, late on Saturday. “There are reports that some people who fled the hospital have been shot at, wounded and even killed.” More than 11,000 Palestinians have now been killed during the Israeli air and ground offensive, and many more wounded, according to the Hamas-run health authorities in Gaza. The dead include more than 4,500 children and more than 3,000 women, Officials from the health ministry said 13 Palestinians were killed in an Israeli strike on a house in Khan Younis, in southern Gaza, on Sunday. A correspondent for Al Jazeera TV network reported that one of the family members who survived the attack said “the ground was shaking underneath their feet before the explosion took place and destroyed the building”. The claims have not been independently verified. Khan Younis is in the south of the Gaza Strip, and is inside the area to which Israel’s military has been directing Palestinians to evacuate. The military wing of Hamas’s ally Islamic Jihad, the al-Quds Brigades, said they were “engaged in violent clashes in the vicinity of al-Shifa medical complex” as well as several other locations in the northern part of Gaza, while a Hamas health official claimed that an Israeli airstrike destroyed the cardiac ward of the hospital. Witnesses confirmed a blast at the hospital, which the Guardian was unable to independently verify. Israel has cut most supplies of electricity, fuel, water and food to Gaza, causing acute suffering to the population of 2.3 million. Many are now crammed into private homes, makeshift shelters in schools and other accommodation in deteriorating conditions. Many lack clean water, appropriate treatment for chronic medical conditions and food. In some shelters, hundreds share a single toilet, with poor hygienic conditions leading to the outbreak of infectious diseases. Commentators in Israel said Israel was winning the military campaign but losing the battle for global public opinion. Netanyahu has said any ceasefire must be conditional on the prior release of all the 240 or more hostages taken by Hamas and other groups during the attacks the militant organisation launched into Israel last month which killed 1,200. Most victims were civilians, killed in their homes or at a dance party. The French president, Emmanuel Macron, urged Israel on Friday to “stop this bombing” in Gaza and said: “There is no other solution than first a humanitarian pause, going to a ceasefire, which will allow [us] to protect … all civilians having nothing to do with terrorists.” On Friday, Antony Blinken, the US secretary of state, said “far too many Palestinians have been killed” in Gaza. There is domestic pressure too on Netanyahu, who announced the deaths of five more Israeli soldiers in Gaza. The Israeli military said 46 had been killed since its ground operations there began. Though there remains overwhelming support for the war among Israelis, the issue of how to obtain the release of the hostages held by Hamas in Gaza is more divisive. Thousands joined a rally outside the Tel Aviv Museum Square, which has been informally renamed “Hostages Square”, to support families of the hostages late Saturday, while Israel’s three major TV news channels, without citing named sources, said there had been some progress toward a deal to win their release. Netanyahu said he would not discuss details of any possible deal, which according to N12 News would involve 50 to 100 women, children and elderly being released in stages during a three- to five-day pause in fighting. According to the reports, Israel would release women and minor Palestinian prisoners and consider letting fuel in to Gaza, while reserving the right to resume fighting. “There will be no ceasefire without the return of our hostages,” Netanyahu told Israelis on Saturday.