Palestinians on Monday fled heavy battles in Gaza City as the Israeli military expanded an evacuation order nine months into its war with Hamas militants.
While fighting raged, Hamas and Israel staked their claims for truce talks as mediators Egypt and Qatar were due to host new meetings this week, according to officials.
Israeli troops and tanks pushed into parts of Gaza City, in the besieged territory's north, and battled Palestinian militants.
Thousands were on the move again, according to the Civil Defence agency in the Hamas-run territory. Witnesses said messages on loudspeakers urged civilians to leave Gaza City's Al-Daraj and Al-Tuffah neighbourhoods.
AFP photographers saw Palestinians leave on foot, bikes and on donkey carts, carrying their belongings through rubble-strewn streets.
Muhammad Bisan said he had been through "an indescribable night" in Gaza City.
"Planes and artillery are bombing and drones are firing from all directions, and we do not know where to run, right or left," he told AFP.
Elsewhere in Gaza, AFPTV images showed Palestine Red Crescent members removing a body from the rubble after a strike in Jabalia, another Gaza City district.
Israel's military reported strikes on targets in the Rafah and Khan Yunis areas of southern Gaza.
The war started with Hamas's October 7 attack on southern Israel that resulted in the deaths of 1,195 people, mostly civilians, according to an AFP tally based on Israeli figures.
The militants 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 38,193 people in Gaza, also mostly civilians, according to data from the territory's health ministry.
The toll includes at least 40 deaths over the previous 24 hours, it said.
Diplomatic efforts to halt the fighting aim for an initial six-week ceasefire that would see some hostages in Gaza freed in exchange for Palestinian prisoners in Israeli jails, but talks would continue for a comprehensive deal to end the war.
Hamas has signalled it would drop its insistence on a "complete" ceasefire, a demand Israel has repeatedly rejected.
A top Hamas official, speaking on condition of anonymity, told AFP that mediators had offered assurances "that as long as the... negotiations continued, the ceasefire would continue".
Israeli Prime Minister Benjamin Netanyahu's office reiterated in a statement that "any deal will allow Israel to return and fight until all the goals of the war are achieved".
The military said Israeli forces were carrying out a "counterterrorism operation" against Hamas and Islamic Jihad militants in the area of the Gaza City headquarters of the United Nations agency for Palestinian refugees, UNRWA.
There was no immediate comment from UNRWA, whose facilities across Gaza have come under attack before.
In Gaza City's Shujaiya district, where battles have raged for nearly two weeks, the military said it had "eliminated dozens" of militants including in air strikes.
Israel in early January said it had dismantled Hamas's "military framework" in northern Gaza, but militants have since regrouped -- pointing to the difficulty of destroying the group which Netanyahu says is one of the goals.
Gaza's Civil Defence reported "dozens of martyrs and wounded" across the coastal territory, saying rescuers were unable to reach some areas due to the intense fighting.
A Hamas senior official on Monday accused the Israeli premier of stepping up bombardment in order to derail the latest truce effort.
"Whenever a round of negotiations begins and a breakthrough is within reach, he... escalates the aggression," the Hamas official charged, speaking on condition of anonymity.
Two separate strikes, on Saturday in the central Nuseirat refugee camp and on Sunday in Gaza City, killed people in schools turned into displacement shelters.
The United Nations estimates 90 percent of Gazans have fled their homes.
Netanyahu's hard-right political allies have threatened to leave the government if he agrees to stop the fighting before Hamas is eliminated.
Israelis rallied again on Sunday in Tel Aviv and Jerusalem, demanding a hostage release deal and new elections in a "Disruption Day" to step up their pressure.
"Our message to the government is very simple," said demonstrator Yehuda Cohen, the father of kidnapped soldier Nimrod Cohen. "There is a deal on the table. Take it."
Egypt's state-linked Al-Qahera News said Cairo would host Israeli and US delegations in a new push in the months-long effort toward a truce.
Israel has said it would also be sending negotiators to Qatar, and an official with knowledge of the mediation said US Central Intelligence Agency (CIA) director William Burns would also go to the Gulf emirate this week.
Israel has exchanged near daily cross-border fire with Hamas's Lebanese ally Hezbollah, raising fears of all-out war as such exchanges escalate.
Israel on Saturday struck deep inside eastern Lebanon, killing a Hezbollah operative, an attack that sparked major rocket and drone barrages by the Iran-backed movement.
On Monday, the Israeli said an air strike had killed a Hezbollah operative in southern Lebanon. Hezbollah announced the fighter's death without elaborating.
