The Israeli military had no immediate comment on the report of the 10 deaths in Jabalia in the north of the war-shattered Gaza Strip.
GHF, which last week started handing out meals to hungry Palestinians inside Gaza, said that a reopening date would be announced later.
The organisation bypasses traditional relief agencies and has been criticised by humanitarian organisations, including the United Nations, for alleged lack of neutrality, which it denies.
The Israeli military said on Sunday and Monday that its soldiers had fired warning shots. On Tuesday, it said, forces also fired warning shots before firing towards Palestinians that it said were advancing towards troops. GHF has said that aid was safely handed out from its sites without any incident.
Israel has re-intensified an offensive against Gaza's dominant Hamas militant group since breaking a two-month-old ceasefire in March in a war triggered by Hamas' cross-border attack on October 7, 2023.
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