The Israeli military said 107 trucks carrying flour and other foodstuffs as well as medical supplies entered the Gaza Strip from the Kerem Shalom crossing point on Thursday.
But getting the supplies to people sheltering in tents and other makeshift accommodation has been fitful.
So far, an umbrella network of Palestinian aid groups said, 119 aid trucks have entered Gaza since Israel eased its blockade on Monday in the face of an international outcry.
But distribution had been hampered by looting by groups of men, some of them armed, near the city of Khan Younis, the network said.
"They stole food meant for children and families suffering from severe hunger," the network said on Friday in a statement that also condemned Israeli air strikes on security teams protecting the trucks.
A Hamas official said six members of a security team tasked with guarding the shipments were killed.
There was no immediate comment from the Israeli military.
The aid groups network also said the amount of aid coming into Gaza was still inadequate and only included a narrow range of supplies.
It said Israel's agreement to allow trucks to enter the war-shattered enclave was a "deceptive manoeuvre" to avoid international pressure calling for the lifting of the blockade.
So far, Israel says it has allowed about 300 trucks to enter Gaza but aid groups say many of the trucks have been held up at the Kerem Shalom crossing and not yet reached people in need.
The Israeli military said it had conducted more strikes in Gaza overnight, hitting 75 targets, including weapons storage facilities and rocket launchers.
Palestinian medical services said at least 25 people had been killed in the strikes.
Israel imposed its blockade on Gaza in early March, accusing Hamas of stealing aid intended for civilians, shortly before breaking a two-month-old ceasefire after the two sides deadlocked on terms for extending it.
Hamas has rejected the accusation and says many of its own fighters have been killed protecting the trucks from looters.
Israel launched an air and ground war in Gaza after Hamas militants' cross-border attack on October 7, 2023, which killed some 1200 people by Israeli tallies and saw 251 hostages abducted into Gaza.
The Israeli campaign has since killed more than 53,600 Palestinians, according to Gaza health authorities, and devastated the coastal strip.
Aid groups say signs of severe malnutrition are widespread.
