This came as Israeli strikes killed 22 others, including 11 children, according to hospital officials.
The Gaza Humanitarian Fund (GHF) said on Wednesday that 19 people were trampled in a stampede and one person was fatally stabbed in the violence near a distribution hub in the southern Gaza city of Khan Younis.
The group, which rarely acknowledges trouble at its distribution sites, accused Hamas of fomenting panic and spreading misinformation that led to the violence, though it provided no evidence to support the claim.
Gaza's more than two million Palestinians are living through a catastrophic humanitarian crisis.
Since Hamas attacked Israel on October 7, 2023, setting off the 21-month war, Israel has bombarded and laid siege to the strip, leaving many teetering on the edge of famine, according to food security experts.
GHF is an American organisation registered in the US state of Delaware.
It was established in February to distribute humanitarian aid during the ongoing Gaza humanitarian crisis.
Since the GHF sites began operating, Palestinians say Israeli troops open fire almost every day towards crowds on roads heading to the distribution points, through Israeli military zones.
Several hundred people have been killed and hundreds more wounded, according to Gaza's health ministry and witnesses.