Israel has cut supplies of food, water and power to Gaza and insisted no fuel can be imported as it could be used by Hamas.
EU leaders have demanded "humanitarian corridors and pauses" in Israel's war against Hamas, urging aid access for civilians trapped in besieged Gaza, where the United Nations says "nowhere is safe."
Concern is growing about the regional fallout from the conflict, with Washington warning Iran against escalation while striking facilities in Syria it says were used by the Iranian Revolutionary Guard Corps and others.
Israel has carried out relentless strikes on Gaza since Hamas gunmen stormed across the border on October 7, killing 1,400 people, mostly civilians, in the deadliest attack since Israel's creation.
The Israeli strikes have killed more than 7,000 people, mostly civilians, according to the Hamas-run health ministry, with growing calls for protection of innocents caught in the conflict.
Late Thursday, EU leaders called for "continued, rapid, safe and unhindered humanitarian access and aid to reach those in need through all necessary measures including humanitarian corridors and pauses for humanitarian needs".
Just 74 trucks of food, water and medicine have been permitted to enter Gaza, home to 2.4 million people, since the conflict began -- a figure described by aid groups as vastly insufficient.
Before the conflict, around 500 trucks entered daily, according to the United Nations.
Israel has cut supplies of food, water and power to Gaza and insisted no fuel can be imported as it could be used by Hamas.
That has forced 12 of the territory's 35 hospitals to close, and the UN agency for Palestinian refugees UNRWA has started to "significantly reduce its operations."
"Without fuel, there will be no humanitarian response, no aid reaching people in need, no electricity for hospitals, no access to clean water, and no availability of bread," UNRWA Commissioner-General Philippe Lazzarini said.
Israel defends its operations, with staunch backing from allies including Washington, and has demanded Hamas release 224 foreign and Israeli hostages it seized on October 7.
The fate of the hostages remains a complicating factor for Israel's planned ground operation.
Hamas's armed wing said Thursday that "almost 50" Israeli hostages had been killed in Israeli bombing raids, a claim that AFP could not verify.
Four hostages have been released, but for relatives of those left behind, the anguish continues.
"Our lives stopped," said Moran Betzer Tayar, of the day her nephew and his wife were abducted.
She told a press conference in France she was "worried sick" and desperate to keep the fate of the hostages in the public eye.
Rights groups and international organisations have demanded the immediate release of hostages, who include women and children.
Inside Gaza, the punishing strikes have left people "with nothing but impossible choices" the UN's humanitarian coordinator for the occupied Palestinian territory said Thursday.
"Nowhere is safe in Gaza," Lynne Hastings said in a statement.
Israel has repeatedly urged civilians in northern Gaza to move south for their safety, but strikes have also hit southern areas and evacuation routes, Hastings said.
Around 45 percent of all housing in Gaza has been damaged or destroyed, according to the UN, citing local authorities, and satellite images show vast swathes of destruction.
Rahma Saqallah fled south with her family, heeding Israeli warnings. But after strikes killed her husband and three of her children, she was heading back home.
"Wherever we go, we will die," she told AFP, as she prepared to leave the southern city of Khan Yunis to return to Gaza City with her surviving child.
"They told us to leave for the south and then they killed us (here)."
Hamas on Thursday released a list of almost 7,000 names of people it said had been killed in Israeli strikes, after US President Joe Biden cast doubt on the toll from the territory.
The list of 6,747 names gave the age, sex and identity card number of each victim, adding that 281 bodies had not yet been identified. Another 1,600 people, including 900 children, are missing and may be under rubble, according to the UN, citing local authorities.
The war's surging death toll is by far the highest since Israel unilaterally withdrew from the coastal territory in 2005 -- a period that has seen four previous Gaza wars.
The situation has been exacerbated by dire medical shortages, with operations now carried out without anesthetic and ice-cream trucks turned into makeshift morgues.
There are fears that the toll will grow exponentially if Israel launches a ground operation that Prime Minister Benjamin Netanyahu says is being prepared.
Israeli troops entered northern Gaza on Wednesday for a "targeted raid" that came in "preparation for the next stages of combat", the military said.
Israel faces growing calls to ensure its response does not cause increasing civilian casualties.
"Israel has to do everything in its power, as difficult as it is, to protect innocent civilians," Biden said this week.
An expansion of fighting on the ground also risks a wider regional conflagration, with Iran's foreign minister warning US officials and military.
"We do not welcome the expansion and scope of the war in the region," Hossein Amir-Abdollah said at the UN.
"But I warn if the genocide in Gaza continues, they will not be spared from this fire."
American and allied forces in Iraq and Syria have been attacked at least 16 times this month, according to the Pentagon, which blamed Iranian-backed groups.
And the US military struck two facilities in eastern Syria used by Iranian forces and affiliated groups, Defence Secretary Lloyd Austin said Thursday, stressing they were "separate and distinct" from the Israel-Hamas conflict.
Biden also sent a rare "direct message" to Iran's supreme leader warning against further escalations, the White House said.
"My warning to the Ayatollah was that if they continue to move against those troops, we will respond, and he should be prepared. It has nothing to do with Israel," Biden said.
Exchanges of fire across the Israel-Lebanon border have prompted the evacuation of tens of thousands of people on either side.
And six people were wounded after a rocket fired in the conflict hit the Egyptian border town of Taba on Thursday, Egyptian media reported.