In what appeared to be the biggest ground assault in Gaza since a truce with Hamas unravelled last week, Israel said its troops – who were backed by warplanes – had reached the heart of Khan Younis and were also surrounding the city.

“We are in the most intense day since the beginning of the ground operation,” the commander of the Israeli military’s Southern Command, General Yaron Finkelman, said in a statement.

He said Israeli forces were also fighting in Jabalia, a large urban refugee camp and Hamas hotbed in northern Gaza next to Gaza City, and in Shuja’iyya, east of the city.

Hamas’ armed wing, the al Qassam Brigades, said its fighters had destroyed or damaged 24 Israeli military vehicles and snipers had killed or wounded eight Israeli soldiers in ongoing clashes in various areas of Khan Younis.

Separately, Gaza health officials said large numbers of people were killed in an Israeli strike on houses in Deir al-Balah, north of Khan Younis. Dr Eyad Al-Jabri, head of the Shuhada Al-Aqsa Hospital there, told Reuters at least 45 were killed. Reuters could not reach the area or confirm the toll.

After days of ordering residents to flee the area, Israeli forces dropped new leaflets on Tuesday with instructions to stay inside shelters during the assault.

“For your safety, stay in the shelters and the hospitals where you are. Don’t get out. Going out is dangerous. You have been warned,” said the leaflets, addressed to residents of six districts amounting to around a quarter of Khan Younis.

“Sixty days after the war began, our forces are now encircling the Khan Younis area,” said Lieutenant General Herzi Halevi, chief of Israel’s General Staff, referring to the October 7 Hamas incursion into Israel that triggered the conflict.

“We have secured many Hamas strongholds in the northern Gaza Strip, and now we are operating against its strongholds in the south,” Halevi told a press conference.

Israel unleashed its campaign in retribution for an attack by Hamas fighters who rampaged through Israeli towns, killing 1200 people and seizing 240 hostages, according to Israel’s tally.

Since then more than 16,248 Palestinians are confirmed to have been killed by Israeli air and strikes and other actions, and the toll is rising each day, according to Gaza health officials. Thousands more are missing and feared buried under rubble.

“We’re moving ahead with the second stage now. A second stage that is going to be difficult militarily,” Israeli government spokesperson Eylon Levy said.

Israel, he added, is open to “constructive feedback” on reducing harm to civilians as long as the advice is consistent with its aim of destroying Gaza’s ruling Islamist movement.

The US has again pressed Israel, its close ally, to uphold international humanitarian law and do more to reduce harm to civilians in the war’s next phase. Despite the mounting death toll, it said Israel was now showing some receptiveness to the calls.

Israeli bombardments have driven 80 per cent of Gaza’s 2.3 million residents from their homes, most fleeing south. Crowded southern areas are now sheltering triple their usual population.

At Khan Younis’ main Nasser hospital, the wounded arrived by ambulance, car, flatbed truck and donkey cart after what survivors described as a strike on a school being used as a shelter for the displaced.

Inside a ward, almost every inch of floor space was taken up by the wounded, with medics hurrying from patient to patient while relatives wailed.

Since the truce collapsed, Israel has been posting an online map to tell Gazans which parts of the enclave to evacuate. Khan Younis’ eastern quarter was marked on Monday, home to hundreds of thousands of people, many of whom took flight on foot.

Gazans say there is no safe place, with remaining towns and shelters already overwhelmed, and Israel continuing to bomb the areas where it is telling people to go.