Israeli ground forces were battling Hamas fighters deep inside Gaza's largest city, Israel said Tuesday. The push signals 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 for "an indefinite period" pointed to the uncertain endgame of a war that Israel says will be long and difficult.

Israeli ground troops have battled Palestinian militants inside Gaza for over a week, cutting the territory in half and encircling Gaza City. The army's chief spokesperson, Rear Adm. Daniel Hagari, said Israeli ground forces "are located right now in a ground operation in the depths of Gaza City and putting great pressure on Hamas."

Hamas spokesperson Ghazi Hamad, speaking Tuesday from Beirut, denied that Israeli forces were making any significant military gains or that they had advanced deep into Gaza City.

"They never give the people the truth," Hamad said. He added that numerous Israeli soldiers were killed Monday and "many tanks were destroyed."

"The Palestinians fight and fight and fight against Israel, until we end the occupation," said Hamad, who left Gaza days before Hamas' Oct. 7 incursion in southern Israel, which sparked the war.

The Associated Press could not independently verify the claims of either side.

Israelis commemorated the 30th day - a milestone in Jewish mourning - since the Hamas incursion, which killed 1,400 people. About 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 as rockets were continuously fired into Israel.

Hundreds of family members of the hostages held in Gaza joined supporters Tuesday beside the Western Wall in Jerusalem to call for the release of their loved ones.

"The hostages have been underground in Gaza for 32 days. I cry out to every single person here and every single person on the planet to make it your mission to free these souls," said Rachel Goldberg, a prominent spokesperson for the hostage families, her voice breaking.

A month of relentless bombardment in Gaza since the Hamas attack has killed more than 10,300 Palestinians - two-thirds of them women and minors, according to the Health Ministry of the Hamas-run territory. More than 2,300 are believed to be buried from strikes that reduced entire city blocks to rubble.

Around 70% of Gaza's 2.3 million people have fled their homes, and many of them are crowded into schools-turned-shelters run by the United Nations. 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.

Fleeing South

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.

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. 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.

From The Associated Press