The aid plan, which has been endorsed by Israel but rejected by the UN, appeared to be unfolding amid fierce Israeli attacks on the enclave, including on a school building where dozens of Palestinians sheltering inside were killed.
Palestinians reported no sign of aid deliveries earlier on Monday, but the Gaza Humanitarian Foundation (GHF) later confirmed that distribution to civilians had begun, a day after its chief unexpectedly stepped down.
"More trucks with aid will be delivered tomorrow, with the flow of aid increasing each day," it said in a statement.
With food critically short after a nearly three-month blockade, Washington says it is working to restore a ceasefire more than 19 months into the war, but progress is elusive.
A Palestinian official said Hamas had agreed to a US proposal for a truce and the release of 10 Israeli hostages, but an Israeli official dismissed the proposal as unacceptable, denying it was Washington's suggestion.
US special envoy Steve Witkoff rejected reports that Hamas had agreed to his proposal, telling Reuters that what he has seen was "completely unacceptable".
Israel has faced a mounting international outcry this month, including from Western allies, as it launched a new offensive in Gaza, already largely destroyed by Israeli bombardment and where the population of two million is at risk of famine.
Close ally Germany said Israel's recent attacks in Gaza were inflicting a toll on civilians that could no longer be justified as a fight against Hamas, which ignited the war with its cross-border October 7, 2023, attack on Israel.
Israeli authorities last week allowed a trickle of aid into the Palestinian enclave for the first time since March. But the few hundred trucks carried a tiny fraction of the food needed.
The GHF's executive director, Jake Wood, announced his resignation on Sunday, saying the foundation could not adhere "to the humanitarian principles of humanity, neutrality, impartiality, and independence".
The Switzerland-registered foundation said on Monday it had appointed John Acree as interim executive director, describing him as a "senior humanitarian practitioner" with over two decades of field experience in disaster response and civil-military co-ordination.
The GHF has been heavily criticised by the United Nations, whose officials have said the private company's aid distribution plans are insufficient.
The new operation will rely on four major distribution centres in southern Gaza that will screen families for involvement with Hamas militants, potentially using facial recognition or biometric technology, according to aid officials.
Hamas condemned the new system, saying it would "replace order with chaos, enforce a policy of engineered starvation of Palestinian civilians, and use food as a weapon during wartime".
Israel says the system is aimed at separating aid from Hamas, which it accuses of stealing and using food to impose control over the population.
In Gaza City, medics said 30 Palestinians, including displaced women and children who were seeking shelter in a school, were killed in an airstrike.
Israel's military confirmed it had targeted the school. It said the building was being used as a centre by Hamas and Islamic Jihad militants to plan and organise attacks.
Farah Nussair, who survived the attack, said "just the tired ones" who needed food and water were in the school.
"We fled to the south, they bombed us in the south. We returned to the north, they bombed us in the north. We came to schools ... There is no security or safety, neither at schools, nor hospitals - not anywhere."
