KHAN YOUNIS, Gaza Strip — Israel said Tuesday that its ground forces were battling Hamas fighters deep inside Gaza’s largest city, signaling a major new stage in the month-old conflict, and its leaders foresee controlling the enclave’s security after the war.

The push into Gaza City guarantees that the already staggering death toll will rise further, while comments from Prime Minister Benjamin Netanyahu about controlling Gaza’s security pointed to the uncertain endgame of a war that Israel says will be long and difficult.

Israelis commemorated the 30th day — a milestone in Jewish mourning — since Hamas militants killed 1,400 people during an Oct. 7 rampage in southern Israel that sparked the war. Some 240 people Hamas abducted during the attack remain in Gaza, and more than 250,000 Israelis have evacuated homes near the borders of Gaza and Lebanon amid continuous rockets fired into Israel.

A month of relentless bombardment in Gaza has killed more than 10,300 Palestinians, two-thirds of them women and minors, according the Health Ministry of the Hamas-run territory. More than 2,300 are believed buried from strikes that reduced entire city blocks to rubble. Around 70% of Gaza’s 2.3 million people have fled their homes, and more than 700,000 of them are crowded into U.N. schools-turned-shelters. Civilians in Gaza are relying on a trickle of aid and their own daily foraging for food and water from supplies that have dwindled after weeks of siege.

Israeli ground troops have battled Palestinian militants inside Gaza for over a week, cutting the territory in half and encircling Gaza City. Chief Israeli military spokesman, Rear Adm. Daniel Hagari, said that Israeli ground forces “are located right now in a ground operation in the depths of Gaza City and putting great pressure on Hamas.”

Speaking in an interview with ABC News that aired late Monday, Netanyahu said the military had killed several thousand Hamas fighters since the war began. The Gaza Health Ministry’s death toll does not distinguish between civilians and combatants — and slain fighters not brought to hospitals would not be in its count.

Israel unleashed another wave of strikes across the Gaza Strip on Tuesday as hundreds more Palestinians fled Gaza City to the south.

Some arrived on donkey carts, most on foot, some pushing elderly relatives in wheelchairs, all visibly exhausted. Many had nothing but the clothes on their backs. “There is no food or drink, people are fighting in the bakeries,” said one man who didn’t want to give his name.

Hundreds of thousands have heeded Israeli orders to head to the southern part of Gaza, out of the ground assault’s path. Others are afraid to do so since Israeli troops control part of the north-south route.

But bombardment of the south has also continued.

An Israeli airstrike destroyed several homes early Tuesday in Khan Younis. An Associated Press journalist at the scene saw first responders pulling five bodies — including three dead children — from the rubble. One man wept as he carried a bloodied young girl, until a rescue worker pried her from his arms, saying, “Let her go, let her go,” to rush her to an ambulance.

AP video at a nearby hospital showed a woman desperately searching for her son, then crying and kissing him when she found him, half-naked and bloodied, but apparently without serious injuries. A girl sobbed next to a baby on a stretcher, apparently dead.