When Israel’s bombs started raining over Gaza, Najla Shawa, a Palestinian humanitarian worker, devised a game to distract her terrified girls, aged six and four.

“We huddle in the corridor and I hug them and together we count out loud the explosions,” she said from her home in the war-scarred strip squeezed between Israel, Egypt and the Mediterranean Sea. “During the first round of bombardment they screamed and screamed, and the eldest began to complain of chest pains. She could not sit or eat because of the fear and tension in her body.”

Trapped in the narrow coastal territory, its borders sealed, Gaza’s civilian population — some 2m people, most of them refugees from previous wars — have nowhere to flee. Israel has pounded the enclave using fighter jets, warships and tanks, while Hamas, the Palestinian militant group, has fired thousands of rudimentary rockets at the Jewish state, though most have been intercepted by the Israeli air defence system.

By Sunday in Gaza 192 people had been killed, including 92 women and children, according to Palestinian health officials. Israel’s military said at least 75 were Hamas militants but did not provide evidence. So far, 10 people have been killed inside Israel, including two children and a soldier.

The number of dead in Gaza is expected to rise, with many still trapped under rubble. On Sunday morning alone Israeli air strikes killed 42 people and collapsed several buildings. Rescuers, using their hands and rudimentary crowbars, struggled to pull the wounded out from twisted metal and heavy concrete, a witness said.

A shortage of ambulances and air strikes on nearby roads meant some survivors had to carry their young children to get medical help. A resident of one apartment block, who asked not to be named, said they had received no warnings to evacuate before it was hit.

Israel insists it is targeting militant positions and has accused Hamas of hiding behind Palestinian civilians. But its military is deploying a higher tempo and intensity of air strikes against a wider range of targets than during previous campaigns, under a new military strategy dubbed the “victory doctrine”. Lt Col Jonathan Conricus of the Israel Defense Forces said one hour-long operation on Thursday night had involved 160 aircraft.

The IDF said the residential buildings that were destroyed on Sunday had collapsed after air strikes had taken out a network of Hamas tunnels nearby, damaging their foundations.

Gaza is one of the most densely populated places in the world and while Hamas fighters can retreat to the tunnels — dug by the group under Gaza’s main cities, towns and refugee camps to help evade air attacks and facilitate communication — civilians have few places to hide.

One Palestinian man described how the building in which his extended family of 30 people lived had swayed from side to side as Israeli shells fell nearby. They fled on Friday at dawn after a nearby home was hit.

“I later heard from neighbours that an entire family, father, mother and four children were buried under the rubble,” he said.

More than 10,000 people have taken shelter in schools run by the UNRWA, the UN agency for Palestinian refugees. Among them, Ahmed Arafat, a farmer from Beit Hanoun in the north-east of Gaza, said he fled with his wife, mother and five children early on Friday to escape shelling from Israeli tanks. During the seven-week 2014 war — the last major conflict between Israel and Hamas — his family had spent a month at a similar shelter. “I don’t know when it will end this time,” he added. “But I am afraid it will last long.”

The Gaza Strip — often likened to an open-air prison by human rights groups — has been blockaded by Israel and Egypt since 2007, when Hamas expelled Fatah, the political faction headed by Mahmoud Abbas, the Palestinian president. With trade and access to the outside world severely restricted, Gaza’s exhausted and impoverished population had already seen their infrastructure crumble and living standards plummet before the latest fighting began.

“Every couple of years there is a conflict of magnitude in Gaza that leaves it even more desperate and destitute than before because of the ongoing blockade,” said Tamara al-Rifai at UNRWA. “Now the health infrastructure which is already weak has to also grapple with Covid-19.”

Power and fresh water supplies, already intermittent in normal times, are in crisis because fuel is no longer getting in. Gaza’s only power plant would run out of fuel by Monday unless a ceasefire was negotiated to allow resupply, an Israeli official said.

Ashraf al-Qudra, at the health ministry in Gaza, said he expected fuel to operate hospital generators to run out in under a week, adding to the pressure on facilities already facing a flood of wounded civilians. More than 1,200 people have been injured.

“We are treating second and third degree burns, people with shattered limbs and others suffering suffocation from poisonous fumes,” he added. “The injuries range from dangerous to life threatening and need surgical interventions that we cannot carry out in Gaza. We need the crossings into Israel to open because they provide a lifeline of necessary medicines, hospital supplies, food and fuel for generators.”

Hamas, an Islamist movement, rules Gaza with an iron fist but there is no evidence yet that Palestinians are blaming the group for the latest suffering. Abbas, the Palestinian president, cancelled planned elections last month in a move widely viewed as motivated by his fear that Hamas would win.

Shawa said her family was watching black smoke waft over the Gaza skyline. Her husband had left their house near the sea in western Gaza only once since the bombing began to get bread. Describing the mood in the territory after years of blockade, she said: “People feel they have nothing to lose and are fed up with this great injustice.”