The GHF, which uses US private security contractors, says it has distributed food packages containing more than 44 million meals since it began operating on 26 May, with more than 2.4 million handed out at three sites on Wednesday.
However, the UN and other aid groups have refused to co-operate with the GHF, accusing it of co-operating with Israel’s goals in a way that violates fundamental humanitarian principles.
They have also expressed alarm at the near-daily reports of Palestinians being killed near the group’s sites, which are inside Israeli military zones.
According to Gaza’s health ministry, at least 549 people have been killed and 4,000 injured while trying to collect aid since the GHF began distributing aid on 26 May.
On Wednesday morning, a spokesman for the Hamas-run Civil Defence agency said six people were killed when Israeli forces opened fire at crowds waiting near one of the GHF’s food distribution centre in central Gaza.
Three others were killed near a GHF site in the southern city of Rafah, he added.
However, the Israeli military said it was “not aware of any incidents with casualties in those areas”, while the GHF said the reports of any such incidents near its sites were false.
In Gaza City, funerals were held for some of the 33 people who the health ministry said had been killed over the previous day while waiting for aid.
“I say and repeat a million times,” Abu Mohammed told Reuters news agency. “These aid points are not aid points, these are death points.”
Unicef spokesman James Elder, who has just visited Gaza, said: “So long as a population is denied food, people are being offered this lethal choice and, unfortunately, because it’s in a combat zone, it cannot improve.”
The Civil Defence spokesman also said another six people, including a child, were killed in an air strike on a house early on Wednesday in Nuseirat refugee camp, in central Gaza.
Five others were killed when homes in the nearby town of Deir al-Balah, he said.