DEIR AL-BALAH, Gaza Strip — Israel said Tuesday that its troops had entered Gaza’s second-largest city as intensified bombardment sent streams of ambulances and cars racing to hospitals with wounded and dead Palestinians, including children, in a bloody new phase of the war.

The military said its forces were “in the heart” of Khan Younis, which has emerged as the first target in the expanded ground offensive into southern Gaza that Israel says aims to destroy Hamas. Military officials said they were engaged in the “most intense day” of battles since the ground offensive began more than five weeks ago, with heavy firefights also taking place in northern Gaza.

The assault into the south is triggering a new wave of displaced Palestinians almost two months into the war, raising warnings from relief groups that they can’t keep up because supplies are insufficient and combat prevents distribution. The U.N. said 1.87 million people — more than 80% of Gaza’s population — have been driven from their homes. New military evacuation orders are squeezing people into ever-smaller areas of the tiny coastal strip’s south.

Bombardment has grown fiercer across the territory, including areas where Palestinians are told to seek safety. In the central Gaza town of Deir al-Balah, just north of Khan Younis, a strike Tuesday destroyed a house where dozens of displaced people were sheltering. At least 34 people were killed, including at least six children, according to an Associated Press reporter at the hospital who counted the bodies.

Israel’s assault in retaliation for Hamas’s Oct 7 attack has killed more than 15,890 people in Gaza — 70% of them women and children — with more than 42,000 wounded, according to the Health Ministry in Gaza. The ministry does not differentiate between civilian and combatant deaths. It says hundreds have been killed or wounded since a weeklong cease-fire ended Friday, and many still are trapped under rubble.

Israel says it must remove Hamas from power to prevent a repeat of the attack that ignited the war, when Hamas and other Palestinian fighters killed about 1,200 people, mostly civilians, and took some 240 captive.

Prime Minister Benjamin Netanyahu said Tuesday that the military would have to retain open-ended security control over the Gaza Strip long after the war ends. His comments suggested a renewed direct Israeli occupation of Gaza, something the United States says it opposes.

Netanyahu said only the Israeli military can ensure Gaza remains demilitarized.

“No international force can be responsible for this,” he said. “I’m not ready to close my eyes and accept any other arrangement.”

Under U.S. pressure to prevent further mass casualties, Israel says it is being more precise as it widens its offensive and is taking extra steps to urge civilians to evacuate out of its path. Weeks of bombardment and a ground offensive obliterated much of northern Gaza.

The military accuses Hamas of using civilians as human shields when operating in dense residential areas. But Israel has not provided accounting for targeting in individual strikes, some of which have leveled entire city blocks and complexes of dozens of multistory apartment towers.

Military Chief of Staff Herzi Halevi acknowledged that Israeli forces use heavy force against civilian structures, saying militants keep weapons in houses and buildings so fighters in civilian clothes can use them to fire on troops.

“Striking them requires significant use of fire, both to target the enemy but also to, of course, protect our forces,” he said.

Halevi said his forces had begun the “third phase of the ground operations,” moving against Hamas in the south after seizing much of the north.

Residents said troops advanced to Bani Suheila, on Khan Younis’ eastern edge. Israeli forces also appear to be moving to partially cut across the strip between Khan Younis and Deir al-Balah. Satellite photos from Sunday showed around 150 Israeli tanks, armored personnel carriers and other vehicles on the main road between the two cities.

The past days brought some of the heaviest bombardment of the entire war, the U.N.’s humanitarian affairs office OCHA said.

Witnesses said a strike Tuesday hit a school in Khan Younis where hundreds of displaced people were sheltering. Casualties overwhelmed the nearby Nasser Hospital, where wounded men and children were lain on a bloody floor amid a tangle of IV tubes.

“What’s happening here is unimaginable,” said Hamza al-Bursh, who lives near the school. “They strike indiscriminately.”

In northern Gaza, the military said its troops were battling Hamas fighters in the Jabaliya refugee camp and the district of Shujaiya, capturing Hamas positions and destroying rocket launchers and underground infrastructure.

The battles in the north signaled the tough resistance from Hamas since Israeli forces moved in Oct. 27. The military says 86 of its soldiers have been killed in the Gaza offensive and that thousands of Hamas fighters have been killed, though it has not produced evidence.

Even after weeks of bombardment, Hamas’ top leader in Gaza, Yehya Sinwar — whose location is unknown — was able to conduct complex cease-fire negotiations and orchestrate the release of more than 100 Israeli and foreign hostages in exchange for 240 Palestinian prisoners last week. Palestinian militants have also kept up their rocket fire into Israel.