The Israeli military said in a statement that troops had opened fire in southern Gaza but said that it had directed warning shots at a group that was moving towards soldiers and deemed a threat to them.
It was the latest bout of shooting near aid distribution points in Gaza's south since a controversial Israeli- and US-backed group, the Gaza Humanitarian Foundation, began handing out aid late in May.
Palestinian paramedics said they had evacuated the bodies of four people who were killed early on Sunday near an aid distribution venue in the southern Gaza city of Rafah.
Media affiliated with Gaza's dominant Hamas militant group reported that the Israeli military had opened fire near a distribution site in Rafah operated by the foundation.
The Israeli military statement said the people towards whom warning shots were fired before dawn on Sunday had been verbally warned to leave the area, which was considered an active military zone at the time.
The military has said people should only move to and from the distribution centres between 6am and 6pm, with non-daylight hours considered a closed military period.
The military acknowledged reports of injuries but did not specify how many people it believed had been hurt or shot.
Sanaa Doghmah said her husband, Khaled, 36, was fatally shot in the head while trying to reach a distribution site in Rafah to collect food for their five children.
"He was going to get food for his children and himself, to make them live, feed them because they don't have a pinch of flour at home," Khaled's aunt, Salwah, said at his funeral.
The foundation, which is handing out aid under an Israeli initiative that is bypassing traditional relief agencies who say their deliveries into Israeli-blockaded Gaza have been restricted, did not immediately respond to requests for comment.
The US-based organisation earlier said in a Facebook post that aid was distributed in central and southern Gaza on Sunday.
It had handed out no aid on Saturday, accusing Hamas of making threats that "made it impossible" to operate in the enclave, which the Islamist group denied.
The foundation uses private American military contractors to operate its sites and has been accused of a lack of neutrality and independence by the United Nations and other international humanitarian agencies.
It has denied such accusations.
Israel relented to international pressure to allow limited UN-led operations to resume on May 19 after an 11-week blockade in the enclave of 2.3 million people, where experts have warned a famine looms.
The UN has described the aid allowed into Gaza as a "drop in the ocean".
While the foundation has said there have been no incidents at its so-called secure distribution sites, Palestinians seeking aid have described scenes of disorder and access routes to the sites have been beset by chaos and deadly violence.
Dozens of Palestinians were killed near foundation sites on June 1-3, Gaza health authorities said.
The Israeli military said on Saturday 350 trucks of humanitarian aid belonging to the UN and other international relief groups were transferred this week via the Kerem Shalom crossing into Gaza.
The war erupted after Hamas-led militants took 251 hostages and killed 1200 people, most of them civilians, in the October 7, 2023 attack - Israel's single deadliest day.
Israel's military campaign has since killed more than 54,000 Palestinians, most of them civilians, according to health authorities in Gaza, and flattened much of the coastal enclave.
