Arizona Tribune - One month on, Israel says forces 'in the heart of Gaza City'

"We are in the heart of Gaza City," Gallant told reporters. "Gaza is the largest terrorist base ever built."

He spoke as memorial ceremonies were held 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."

Despite growing calls for a ceasefire, Israeli Prime Minister Benjamin Netanyahu has made clear there will not be one unless Hamas releases the 240 hostages taken in the attack.

Netanyahu also 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.

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 targets in Gaza with more than 12,000 air and artillery strikes and sent in ground forces that have effectively cut the strip in half, with soldiers and tanks tightening the encirclement of Gaza City.

- 'Enough is enough' -

Israel 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 the repeated Israeli air drops of 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. Enough is enough. We are tired."

The suffering in Gaza has been immense, with entire city blocks levelled and bodies in white shrouds piling up outside hospitals where surgeons have had to operate on bloodied floors by the light of their phones.

Following the latest heavy strikes Tuesday, hundreds of residents fled southwards, with Israeli tanks by the roadside behind sand berms.

Military analysts warned of weeks of gruelling house-to-house fighting ahead in Gaza, from which Israel withdrew in 2005 and where it launched its last land incursion in 2014.

"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 Vedant 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 escape through the crossing.

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, speaking to ABC News on Monday, stressed 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 -

Israeli troops stationed near the Gaza border told AFP they felt proud to protect their country but also nervous as the war intensifies.

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.

"This is a very important moment... for the G7 to come together in the face of this crisis and speak as we do in one clear voice," he said at the start of the two-day meeting.

In the occupied West Bank on Sunday, Blinken 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.

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M.Robinson--AT