Heavy combat and bombardment hit Gaza City and other parts of the Palestinian territory, as mediators continue to push on with efforts to halt the war raging into its tenth month.
US President Joe Biden said at a NATO summit in Washington that US diplomats, despite problems, were making "progress" with international mediators towards a ceasefire and stressed that "it's time to end this war".
Media linked to Hamas, whose 7 October attack sparked the bloodiest ever Gaza conflict, said that Israeli forces had launched more than 70 new air strikes.
Gaza's health ministry reported 32 deaths, saying that the "martyrs, a majority of them children and women, were taken to hospitals overnight, because of continued massacres".
Israel's military said it was also fighting in the Rafah area, in the south, where its troops had "eliminated numerous terrorists in close-quarters combat and aerial strikes".
A major focus of recent battles and mass displacement has been the biggest urban area, Gaza City, where two weeks of fighting devastated the eastern district of Shujaiya.
Gaza's civil defence agency said dozens of bodies have been found under the rubble of what was now a "disaster zone", with 85% of buildings uninhabitable.
Gaza City had been the focus of Israeli ground operations early in the war.
Families trapped and seeking security
Israeli troops and tanks have, since Shujaiya, swept into other Gaza City districts to fight Hamas and Islamic Jihad militants, including in the vacated headquarters of the UN agency for Palestinians UNRWA.
The army dropped thousands of leaflets yesterday urging all Gaza City residents to flee the "dangerous combat zone" - an area where the United Nations said up to 350,000 people were staying.
One of the newly displaced, Umm Ihab Arafat, sat with her children on a sand pile amid the rubble as the incessant hum of Israeli drones filled the sky.
"I have been displaced four times," she said, pleading for a break for her and her children. "They are entitled to rest, their eyes are full of horror and fear."
The International Committee of the Red Cross said that "entire families are trapped and desperately seek security. The huge needs are beyond our capacity to respond".
The ICRC said Gaza City's people had been instructed to move south "to areas that are overcrowded, lacking in essential services and are experiencing hostilities".
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Truce talks ongoing in Doha
Israel and Hamas have engaged in months of indirect talks via Qatari and Egyptian mediators to reach a so far elusive truce and hostage release deal.
At the latest meeting in Doha on Wednesday, Israeli and US officials talked conditions for peace with Qatari mediators.
The head of Israel's Shin Bet internal security agency Ronen Bar was headed for talks in Cairo, said Prime Minister Benjamin Netanyahu's office.
Mr Netanyahu again insisted that any deal must allow Israel to meet its war aims of bringing home all hostages and destroying Hamas.
He also said Israel needs to maintain control of Gaza's southern border to prevent "weapons to be smuggled to Hamas from Egypt".
A leading South African judge, whose country has brought Israel to the top world court over Gaza, said "hardly anything" will deter Israel's offensive.
Mr Biden has laid out what he called an Israeli plan which would see a six-week truce in which hostages held in Gaza and Palestinians in Israeli prisons would be freed. A second phase would see talks on a full end to the war.
He acknowledged that "difficult, complex issues" remain but insisted that "we're making progress".
He also stood firm on his decision to hold up delivery of massive 900kg bombs, over concerns they could be used in populated areas, even as his administration moves forward on sending Israel less powerful munitions. He again pressed Israel for a "day-after" plan for Gaza and spoke of his diplomacy to persuade Arab states to help with security.
Hamas has proposed an independent and non-partisan government for both post-war Gaza and the Israeli-occupied West Bank during ceasefire negotiations, said Hossam Badran, a member of the group's political bureau.
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