Officials at the hospital on Sunday said another 175 people were wounded, without saying who opened fire on them. An Associated Press reporter saw dozens of people being treated at the hospital.
The GHF's distribution of aid has been marred by chaos, and multiple witnesses have said Israeli troops fired on crowds near the delivery sites.
Before Sunday, at least six people had been killed and more than 50 wounded according to local health officials.
The foundation says the private security contractors guarding its sites did not fire on the crowds, while the Israeli military has acknowledged firing warning shots.
The foundation did not immediately respond to a request for comment. In an earlier statement, it said it distributed 16 truckloads of aid early on Sunday "without incident".
There was no immediate statement from the Israeli military regarding an attackon Sunday.
Palestinian and Hamas-affiliated media said Israeli troops fired shots during Sunday's relief operation organised by the GHF at a distribution centre in Rafah.
The GHF, also backed by Israel, recently started operating in Gazs after a blockade of aid deliveries lasting three months.
Israel has been allowing a small amount of goods into the sealed-off coastal strip for a few days.
According to the Israeli government, the GHF is to be responsible for distributing aid supplies to the population of Gaza in order to bypass aid organisations from the United Nations and other initiatives.
The UN has criticised the initiative, fearing it will lure the population to the few distribution centres and accelerate their expulsion from other residential areas.
There have been reports of looting and a storming of the new distribution centres in recent days.
The GHF has repeatedly denied reports of deaths, large numbers of injuries and chaotic scenes at the centres.
While some Palestinians expressed concern over its neutrality and biometric and other checks, Israel said it would employ, Israeli officials said it allowed screening of recipients to exclude anyone found to be connected with Hamas.
On May 28, Hamas accused Israel of killing at least three Palestinians and wounding 46 near one of the GHF's distribution sites, an accusation the aid group denied.
The Israeli military also said its troops fired warning shots in the area outside the compound to re-establish control, as thousands of Palestinians rushed to an aid distribution site.
Hamas is seeking amendments to the latest US ceasefire proposal for Gaza, but President Donald Trump's envoy rejected the group's response as "totally unacceptable".
Israeli officials have approved the US proposal for a temporary ceasefire in the nearly 20-month war.
A Hamas official said proposed amendments focused on "the US guarantees, the timing of hostage release, the delivery of aid and the withdrawal of Israeli forces".
A separate Hamas statement said the proposal aims for a permanent ceasefire, a comprehensive Israeli withdrawal from Gaza and an ensured flow of aid.
It said 10 living hostages and the bodies of 18 others would be released " in exchange for an agreed-upon number of Palestinian prisoners."
Fifty-eight hostages remain and Israel believes 35 are dead.
Trump's special Middle East envoy Steve Witkoff was unimpressed with Hamas' response.
"It is totally unacceptable and only takes us backward. Hamas should accept the framework proposal we put forward as the basis for proximity talks, which we can begin immediately this coming week," he wrote on X.
and AP with dpa
