The GHF says it won't distribute any food on Wednesday and has asked the Israeli military to "guide foot traffic in a way that minimises confusion or escalation risks" near military perimeters; develop clearer guidance for civilians; and enhance training to support civilian safety.
"Our top priority remains ensuring the safety and dignity of civilians receiving aid," a GHF spokesperson said.
An Israeli military spokesperson warned civilians against moving in areas leading to GHF sites on Wednesday, deeming them "combat zones".
The Israeli military said on Tuesday that it opened fire on a group of people it viewed as a threat near a GHF food aid distribution site.
The International Committee of the Red Cross said at least 27 people were killed and dozens injured. The GHF said the incident was "well beyond" its site.
Palestinians who collected food GHF boxes on Tuesday described scenes of pandemonium, with no-one overseeing the handover of supplies or checking IDs, as crowds jostled for aid.
The UN Security Council is also set to vote on Wednesday on a demand for a ceasefire between Israel and Palestinian militants Hamas and humanitarian access across Gaza, where aid has trickled amid chaos and bloodshed after Israel lifted an 11-week blockade on the enclave where famine looms.
"It is unacceptable. Civilians are risking – and in several instances losing – their lives just trying to get food," UN spokesperson Stephane Dujarric said on Tuesday, adding that the aid distribution model backed by the US and Israel was "all a recipe for disaster, which is exactly what is going on".
That model is run by the newly created GHF, which started operations in the enclave a week ago and said on Tuesday that it has given out more than seven million meals from three so-called secure distribution sites.
GHF Interim Executive Director John Acree urged humanitarians in Gaza: "Work with us and we will get your aid delivered to those who are depending on it."
The UN and other aid groups have refused to work with the GHF because they say it is not neutral and the distribution model militarises aid. GHF uses private US security and logistics companies to get aid to the distribution sites.
It is the latest in a string of efforts to get more aid into the enclave, where experts say the entire population of some 2.1 million people is at risk of famine.
The UN has long-blamed Israel and lawlessness in the enclave for hindering the delivery of aid into Gaza and its distribution throughout the war zone. Israel accuses Hamas of stealing aid, which the group denies.
Israel said on Tuesday that three of its soldiers had been killed in fighting in northern Gaza.
Gaza health officials said at least 18 more Palestinians were killed in other military strikes in the territory on Tuesday. Reuters could not independently verify the reports in northern and southern Gaza.
The 10 elected members of the UN Security Council have asked for the 15-member body to vote on Wednesday on a draft resolution that demands "an immediate, unconditional and permanent ceasefire in Gaza respected by all parties".
The draft text also demands the release of all hostages held by Hamas and others, and the immediate lifting of all restrictions on the entry of aid and its safe and unhindered distribution, including by the UN, throughout Gaza.
