Heavy combat and bombardment hit Gaza City and other parts of the Palestinian territory on Friday as mediators pushed on with efforts to halt the war raging into its tenth month.
US President Joe Biden said at a NATO summit in Washington on Thursday 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 the territory's rulers Hamas, whose October 7 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 percent of buildings uninhabitable.
Gaza City had been the focus of Israeli ground operations early in the war.
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 Wednesday 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".
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.
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.
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.
Biden acknowledged Thursday that "difficult, complex issues" remain but insisted that "we're making progress".
"The trend is positive," he said, "and I'm determined to get this deal done and bring an end to this war, which should end now."
Biden also stood firm on his decision to hold up delivery of massive 2,000-pound bombs, over concerns they could be used in populated areas, even as his administration moves forward on sending Israel less powerful 500-pound 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.
The war started after Hamas's October 7 attack on southern Israel resulted in the deaths of 1,195 people, mostly civilians, according to an AFP tally based on Israeli figures.
The militants also seized 251 hostages, 116 of whom remain in Gaza, including 42 the military says are dead.
Israel responded with a military offensive that has killed at least 38,345 people in Gaza, also mostly civilians, according to data from the health ministry in Hamas-ruled Gaza.
Israel also imposed a punishing siege on the territory of 2.4 million people, pushing many to the brink of starvation.
The World Health Organization said that only five trucks carrying medical supplies were allowed into Gaza last week, while over 70 more are waiting at the border.
A problem-plagued US effort to get aid in by sea will soon end permanently, the United States military said.
US troops built the $230-million pier but the temporary facility has been repeatedly damaged by poor weather.
Biden said he had been "hopeful that would be more successful".
