Israeli army units are deployed in the "heart of the Gaza City," the country's Defense Minister Yoav Gallant said Tuesday, amid continuous attacks targeting civilian infrastructure in the blockaded enclave, as the U.S. said it opposes the occupation of Gaza.
"The ground forces attacked from all directions with complete coordination with naval and ground forces. They are tightening the stranglehold around Gaza," Gallant said in a televised address.
Israel has launched air and ground attacks on the Gaza Strip following a cross-border attack by the Palestinian group Hamas on Oct. 7.
At least 10,328 Palestinians, including 4,237 children and 2,719 women, have been killed since then. The Israeli death toll, meanwhile, is nearly 1,600, according to official figures.
Besides the large number of casualties and massive displacements, basic supplies are running low for Gaza's 2.3 million residents due to the Israeli siege.
Despite growing calls for a cease-fire, Israeli Prime Minister Benjamin Netanyahu has made clear there will not be one unless the hostages are freed.
He has said Israel would assume "overall security" in Gaza after the war ends while allowing for possible "tactical pauses" before then to free captives and deliver aid to the besieged territory of 2.4 million people.
However, Washington said Tuesday it opposed a new long-term occupation of Gaza by Israel.
"Our viewpoint is that Palestinians must be at the forefront of these decisions and Gaza is Palestinian land and it will remain Palestinian land," said U.S. State Department spokesperson Vedant Patel.
"Generally speaking, we do not support the reoccupation of Gaza and neither does Israel."
Israel withdrew from the territory, which it captured in the 1967 Six-Day War, in 2005.
On Tuesday, U.N. rights chief Volker Turk called the month that followed the attack one marked by "carnage, of incessant suffering, bloodshed, destruction, outrage and despair."
Since the attack, Israel has relentlessly hammered Gaza with over 12,000 air and artillery strikes and sent in ground forces that have effectively cut it in half.
Tel Aviv has air-dropped leaflets and sent texts ordering civilians in northern Gaza to flee south, but also targeted the south and displaced people fleeing.
Clutching one of her toddlers, Amira al-Sakani recounted how she left Gaza City.
On the way, Sakani said she saw "bodies of martyrs, some in pieces, people abandoning their cars and cattle to walk.
"Our life is tragic; we don't want war ... we want peace."
The suffering in Gaza has been immense, with entire city blocks leveled and bodies in white shrouds piling up outside hospitals where surgeons operate on bloodied floors by the light of phones.
The World Health Organization (WHO) said an average of 160 children are killed every day in Gaza by the war.
"The level of death and suffering is hard to fathom," WHO spokesperson Christian Lindmeier told reporters in Geneva.
The International Committee of the Red Cross, which said one of its humanitarian convoys in Gaza was hit by gunfire on Tuesday, demanded an end to the suffering of civilians, especially children.
"Children have been ripped from their families and held hostage. In Gaza, ICRC surgeons treat toddlers whose skin is charred from widespread burns," the organisation's president Mirjana Spoljaric said.
"This is a moral failing," she added.
Military analysts warned of weeks of grueling house-to-house fighting ahead in Gaza.
"Hamas has had 15 years to prepare a dense 'defense in depth' that integrates subterranean, ground-level and above-ground fortifications," said Michael Knights of the Washington Institute think tank.
The operation is hugely complicated for Israel because of the hostages, including very young children and frail elderly people, who are believed to be held inside a tunnel network spanning hundreds of kilometers (miles).
Israel's top ally, the United States, has backed it, but also urged restraint and facilitated some aid deliveries and the flight of several hundred refugees with second passports through the Rafah crossing with Egypt.
Patel said "more than 400 U.S. citizens" have now left Gaza through Rafah.
Hundreds of Palestinians who hold foreign passports waited on Tuesday in Gaza to leave.
While most still queued nervously, the first arrivals were seen on the Egyptian side where paramedics transferred an injured woman on a stretcher into an ambulance.
Tuesday was the fifth day Gaza's sole land crossing not controlled by Israel has opened in the past week, to wounded Palestinians, foreigners and Palestinian dual nationals.
Netanyahu told ABC News on Monday the war would continue until Israel had restored overall control of Gaza.
"Israel will, for an indefinite period ... have the overall security responsibility," he said.
He stressed that "there will be no cease-fire in Gaza, without the release of our hostages.
"As far as tactical, little pauses – an hour here, an hour there – we've had them before.
"I suppose we'll check the circumstances in order to enable goods – humanitarian goods – to come in or our hostages, individual hostages, to leave," he added.
Around 30 Israeli soldiers have been killed in the offensive, the latest on Monday, according to a report from the U.N. Office for the Coordination of Humanitarian Affairs, citing Israeli sources.
U.S. Secretary of State Antony Blinken, after a Middle East tour of crisis diplomacy, was in Tokyo on Tuesday for a meeting of G-7 foreign ministers set to seek a common line on Gaza as calls mount for a cease-fire.
In the occupied West Bank on Sunday, he suggested the Palestinian Authority under President Mahmoud Abbas should retake control.
Abbas said the PA could return to power in Gaza in the future only if a "comprehensive political solution" is found for the Israeli-Palestinian conflict.