Street battles raged in Gaza City with Hamas fighters using tunnels to ambush Israeli forces, as the United States said Palestinians must govern Gaza post-war, countering Israeli comments that it would control security indefinitely.

The Israeli military said its troops had advanced into the heart of Gaza City, Hamas' main bastion and the biggest city in the seaside enclave, while the Islamist group said its fighters had inflicted heavy losses.

Hamas' armed wing on Wednesday released a video that appeared to show intense street battles alongside bombed out buildings in Gaza City.

Israeli tanks have met heavy resistance from Hamas fighters using underground tunnels to stage ambushes, according to sources with Iran-backed Hamas and the separate Islamic Jihad militant group.

Israel struck Gaza in response to a cross-border Hamas raid on southern Israel on Oct. 7 in which gunmen killed 1,400 people, mostly civilians, and took about 240 hostages, according to Israeli tallies.

Palestinian officials said 10,569 people had been killed as of Wednesday, 40% of them children. Israel says 33 of its soldiers have been killed.

Palestinian-led governance

As the Israel-Hamas war enters its second month, Washington has begun discussing with Israeli and Arab leaders a future for the Gaza Strip without Hamas rule.

While a plan has yet to emerge, U.S. Secretary of State Antony Blinken outlined Washington's expectations for the besieged coastal territory.

"No reoccupation of Gaza after the conflict ends. No attempt to blockade or besiege Gaza. No reduction in the territory of Gaza," Blinken said on Wednesday at a press conference in Tokyo.

Blinken said there may be a need for "some transition period" at the end of the conflict, but post-crisis governance "must include Palestinian-led governance and Gaza unified with the West Bank under the Palestinian Authority."

On Monday, Israel's Prime Minister Benjamin Netanyahu told ABC News that Israel will "for an indefinite period" have security responsibility for the enclave after the war.

Israeli officials have since tried to clarify they do not intend to occupy Gaza after the war, but they have yet to articulate how they might ensure security without maintaining a military presence. Israel withdrew its forces from Gaza in 2005.

The Palestinian Authority (PA), which exercises limited self-rule in parts of the Israeli-occupied West Bank, says Gaza, where Hamas has ruled since 2007, is an integral part of what it envisions for a future Palestinian state.

Khalil al-Hayya, a member of Hamas' leadership, told the New York Times that the group's assault on Israel was intended to shatter the status quo and open a new chapter in its fight against Israel.

"We succeeded in putting the Palestinian issue back on the table, and now no one in the region is experiencing calm," he said, according to the newspaper on Wednesday.

Saleh al-Arouri, an exiled Hamas commander, told Hamas-affiliated Al-Aqsa TV on Wednesday that its fighters are determined to inflict losses on Israeli forces in ground battles in Gaza. "The more (Israel) spreads and expands on the ground, the deeper its losses will become", he said.

A clip from the Hamas video released on Wednesday showed fighters in Gaza running past piles of debris and stopping to fire shoulder-propelled missiles at Israeli tanks. Another showed them shooting rifles from perches behind buildings and dumpsters. Reuters was not able to authenticate the footage.

Israel bombs tunnels

Chief Israeli military spokesperson Rear Admiral Daniel Hagari said on Wednesday that "Hamas has lost control in the north" of Gaza.

Israel's combat engineers were using explosive devices to destroy Hamas' tunnel network that stretches for hundreds of kilometres (miles) beneath Gaza, he said. The military said it had destroyed 130 tunnel shafts so far.

Israel has blamed Hamas for civilian deaths in Gaza, saying that it is using Gazans as human shields and hiding arms and operations centres in residential areas.

Israeli troops took foreign reporters to the edges of Gaza City on Wednesday. Journalists saw a devastated landscape where every building within sight was scarred by battle.

Walls were blown away while bullet holes and shrapnel dotted the facades and palm trees were shredded and broken.

Lieutenant Colonel Ido, deputy commander of the 401st Brigade, who did not give his last name, said that by the time soldiers reached these buildings, all the families had left.

"So we know that everyone here is our enemy. We have not seen any civilians here. Only Hamas," he said, standing in a badly damaged children's bedroom that was painted pink.

Soldiers on the press tour said that beneath the family apartment were two floors of workshops used to make weapons, including drones discovered in five wooden boxes. It was not possible to verify the claim.

50,000 Palestinians head south

Some 50,000 Palestinian civilians left the north on Wednesday, Hagari said, during a four-hour window of opportunity announced by Israel.

The Israeli military has repeatedly told residents to evacuate the north or risk being trapped in the violence. At least 19 people were killed in an Israeli airstrike on a house near a hospital in north Gaza's Jabalia refugee camp on Wednesday, the enclave's interior ministry said.

There was no immediate Israeli comment or details on the reported attack, which if confirmed would be the third on Gaza's largest refugee camp in a week.

UN officials and G7 world powers stepped up appeals for a humanitarian pause in the war to assist civilians in Gaza, where necessities including food, medicine and fuel are running out.

Negotiations mediated by Qatar, where several Hamas political leaders are based, are trying to secure the release of 10 to 15 hostages in exchange for a one- to two-day humanitarian pause in Gaza, a source briefed on the talks said on Wednesday.