Israel said Tuesday its forces were operating "in the heart of Gaza City" one month after Hamas's bloody October 7 attacks, as the campaign to crush the Palestinian militants intensifies.
Prime Minister Benjamin Netanyahu also issued a stark warning to Hezbollah in Lebanon which, like Hamas, is backed by Iran.
"If Hezbollah makes the choice of joining the war it will be making the mistake of its life," he said in a televised statement marking a month of the war.
His defence minister, Yoav Gallant, underlined Israel's determination "to destroy Hamas".
"We are in the heart of Gaza City," he told reporters. "Gaza is the largest terrorist base ever built."
Netanyahu also said there would be no fuel delivered to Gaza and no ceasefire in Israel's fighting with Hamas unless the more than 240 hostages seized by the Palestinian militants are freed.
Both men spoke on a day of commemoration in Israel to mark the grim one-month milestone.
Sobs pierced memorial ceremonies and crowds lit candles while mourning the 1,400 dead, including families slain in their homes and young people killed at a music festival, in Israel's worst attack since its 1948 founding.
Israel has vowed to destroy the Islamist militants over their shock attack, launching a campaign in the Gaza Strip that has killed more than 10,300 people, mostly civilians, said the Palestinian territory's Hamas-run health ministry.
"There's not one person not impacted by these horrible attacks," said 52-year-old Sharon Balaban, one of thousands of Israelis who attended sorrowful memorial events. "Everyone knows somebody who was hurt, killed, murdered or impacted."
- US opposes Gaza occupation -
Despite growing calls for a ceasefire, 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 State Department spokesman 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 UN 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 more than 12,000 air and artillery strikes and sent in ground forces that have effectively cut it in half.
- 'Moral failing' -
It has air-dropped leaflets and sent texts ordering civilians in northern Gaza to flee south, but a US official said Saturday at least 350,000 civilians remained in the worst-hit areas.
Clutching one of her toddlers, Amira al-Sakani recounted how she left Gaza City after coming across the air-dropped Israeli flyers.
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 levelled and bodies in white shrouds piling up outside hospitals where surgeons operate on bloodied floors by the light of phones.
The World Health Organization 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 spokesman 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 gruelling house-to-house fighting ahead in Gaza.
"Hamas has had 15 years to prepare a dense 'defence 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 kilometres (miles).
Israel's top ally, the United States, has backed it in its war on Hamas, 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.
- 'Little pauses' -
US State Department spokesman Patel said "more than 400 US 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. "When we don't have that security responsibility, what we have is the eruption of Hamas terror on a scale that we couldn't imagine."
He stressed that "there will be no ceasefire -- general ceasefire -- 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.
- US diplomacy -
Around 30 Israeli soldiers have been killed in the offensive, the latest on Monday, according to a report from the UN Office for the Coordination of Humanitarian Affairs, citing Israeli sources.
US Secretary of State Antony Blinken, after a Middle East tour of crisis diplomacy, was in Tokyo on Tuesday for a meeting of G7 foreign ministers set to seek a common line on Gaza as calls mount for a ceasefire.
In the occupied West Bank on Sunday, he suggested the Palestinian Authority under president Mahmud 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.