The Gazan health authorities said that Israel’s military killed at least 32 people in southern Gaza on Saturday, after Israeli troops had opened fire near a food distribution site.

The Israeli military said in a statement that its troops, positioned roughly 1,000 yards from a food site in Rafah, in southern Gaza, had fired “warning shots” after people approached them and did not comply with an order to halt. The site had not yet opened for the day, the statement added.

The Gaza Humanitarian Foundation, a private Israel-backed group that runs the site, said that there were “no incidents at or near any of our aid distribution sites today.” But it acknowledged that some deadly Israeli military activity had “occurred hours before our sites opened,” most of it “several kilometers away from the nearest G.H.F. site.”

Though the foundation has told civilians to avoid the sites before they open, Palestinians often head there early because the food often runs out quickly, sometimes walking for long hours to reach the aid points.

The bloodshed was the latest episode of violence connected to a new and deeply contentious food distribution system in Gaza that was introduced by Israel nearly two months ago. The United Nations said this past week that more than 670 Palestinians had been killed over the past two months near sites run by the Gaza Humanitarian Foundation.

Since the system was implemented in late May, the Israeli military has mandated that the foundation distribute food to Palestinians from a handful of sites in areas under Israeli control. The system largely replaces one run by the United Nations, which previously distributed food from hundreds of points, mainly in areas controlled by the Palestinian militant group Hamas.