Israeli Prime Minister Benjamin Netanyahu said that the military is dividing Gaza and "seizing territory" to force Hamas to free hostages held in the Palestinian territory.
The military is "dissecting the (Gaza) Strip and increasing the pressure step by step so that (Hamas) will return our hostages", Mr Netanyahu said in a statement, adding that Israel "is seizing territory, striking terrorists, and destroying infrastructure".
He added that the army is "taking control of the 'Morag Axis'", a strip of land that is expected to run between the southern governorates of Khan Yunis and Rafah.
The name of the axis refers to a former Israeli settlement in the area that was evacuated during Israel's disengagement from Gaza in 2005.
He likened the new axis to the Philadelphi Corridor, a strip of land along Egypt's border that Israel says it needs to control to prevent weapons smuggling into the Palestinian territory from Egypt.
Mr Netanyahu added that Israel will keep applying military pressure until Hamas frees the remaining hostages.
Of the 251 hostages seized during Hamas's unprecedented 7 October 2023 attack, 58 are still held in Gaza including 34 the Israeli military said are dead.
Israel resumed major air strikes on the Palestinian territory on 18 March, after talks on next steps in a six-week truce broke down.
Since 18 March, at least 1,066 people have been killed in Gaza, according to figures last updated by the Hamas-run territory's health ministry.
In total, 50,423 people have been killed since the start of the war triggered by Hamas's October 2023 attack, according to the ministry's figures, which the United Nations views as reliable.
Seize 'large areas'
Earlier, Israel said it would expand its military operations and seize "large areas" of Gaza where rescuers said 34 people were killed in Israeli strikes, including on a UN building.
Defence Minister Israel Katz said Israel would bolster its military presence in the Palestinian territory to "destroy and clear the area of terrorists and terrorist infrastructure".
The operation would "seize large areas that will be incorporated into Israeli security zones", he said in a statement, without specifying how much territory.
Gaza's civil defence agency said at least 19 people were killed, including nine children, when an Israeli strike "targeted an UNRWA (UN agency for Palestinian refugees) building housing a medical clinic in Jabalia refugee camp".
The Israeli army said in a statement that it struck Hamas militants "inside a command and control centre" in north Gaza's Jabalia. It separately confirmed to AFP the building housed a UN clinic.
The Palestinian foreign ministry, based in the occupied West Bank, condemned the "massacre at the UNRWA clinic in Jabalia" and called for "serious international pressure" to halt Israel's widening offensive.
Israel has on several occasions conducted strikes on UNRWA buildings housing displaced people in Gaza, where fighting has raged for most of the past 18 months.
The Israeli military accuses Hamas of hiding in school buildings where thousands of Gazans have sought shelter - a charge denied by the Palestinian militant group.
Israel also carried out deadly air strikes in southern and central Gaza. The civil defence said dawn strikes killed at least 13 people in Khan Yunis and two in Nuseirat refugee camp.
Mr Katz warned last week that the military would soon "operate with full force" in more parts of Gaza.
In February, he announced plans for an agency to oversee the "voluntary departure" of Palestinians from the territory.
That followed Israel's backing of a proposal from US President Donald Trump for the United States to take over the territory after relocating its 2.4 million Palestinian inhabitants. The proposal outraged Gazans and drew widespread international condemnation.
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'Horrified'
An Israeli group representing the families of hostages still held in Gaza said they were "horrified" by Mr Katz's announcement of expanded military operations.
"Has it been decided to sacrifice the hostages for the sake of 'territorial gains?'" the Hostages and Missing Families Forum asked in a statement.
Mr Netanyahu has rejected suggestions his government is not doing enough to secure the hostages' release.
"We are negotiating under fire... We can see cracks beginning to appear" in Hamas's positions during ceasefire talks, he told his cabinet on Sunday.
'They're all closed'
Hunger loomed in Gaza City as bakeries closed due to worsening shortages of flour and sugar since Israel blocked the entry of aid supplies from 2 March.
"I've been going from bakery to bakery all morning, but none of them are operating, they're all closed," Amina al-Sayed told AFP.
On Sunday, Mr Netanyahu offered to let Hamas leaders leave Gaza but demanded the group abandon its arms.
Hamas has signalled willingness to cede power in Gaza but calls disarmament a "red line".
Egypt, Qatar and the United States are attempting to broker a new ceasefire and secure the release of the remaining Israeli hostages.
A senior Hamas official said on Saturday the group had approved a new ceasefire proposal, while Netanyahu's office said Israel had submitted a counter offer. The details remain undisclosed.
Israel's far-right National Security Minister Itamar Ben Gvir visited Jerusalem's flashpoint Al-Aqsa Mosque compound, drawing condemnation not only from Hamas but also from neighbouring Jordan, which acts as custodian of the holy site.
Mr Ben Gvir has repeatedly challenged the longstanding convention that Jews may visit but not pray at the compound, stoking Palestinian fears about Israeli intentions.
