They called the left-leaning Israeli daily Haaretz's findings "malicious falsehoods designed to defame" the military.
More than 500 Palestinians have been killed and hundreds more wounded while seeking food since the newly formed Gaza Humanitarian Foundation began distributing aid in the territory about a month ago, according to Gaza's health ministry.
Palestinian witnesses say Israeli troops have opened fire at crowds on the roads heading toward the sites.
Reacting to the Haaretz piece, Israel's military confirmed it was investigating incidents in which civilians had been harmed while approaching the sites.
It rejected the article's allegations "of deliberate fire toward civilians".
The foundation, which is backed by an American private contractor, has been distributing food boxes at four locations, mainly in the far south of Gaza, for the past month.
"GHF is not aware of any of these incidents but these allegations are too grave to ignore and we therefore call on Israel to investigate them and transparently publish the results in a timely manner," the group said in a social media post.
Palestinians trying to find food have frequently encountered chaos and violence on their way to and on arrival at the aid sites.
Tens of thousands are desperate for food after Israel imposed a two-and-a-half month siege on Gaza, blocking all food, water and medicine from entering the territory pending the set-up of the GHF sites.
The bodies of eight people who died on Friday had come to Shifa Hospital from a GHF site in Netzarim, although it was not immediately clear how they died, Dr Mohamed Abu Selmyiha, the hospital's director, told The Associated Press.
A GHF spokesperson challenged the report, saying they did not know of any incidents at or near their sites on Friday.
Twenty other bodies his hospital received on Friday came from air strikes across north Gaza, he said.
Thousands of Palestinians walk for hours to reach the hubs, moving through Israeli military zones where witnesses say Israeli troops regularly open fire with heavy barrages to control the crowds.
The Israeli military says it has only fired warning shots.
The group Doctors Without Borders on Friday condemned the distribution system as "a slaughter masquerading as humanitarian aid" and called for it to be immediately shut down.
More than 6000 people have been killed and more than 20,000 injured in Gaza since the ceasefire collapsed on March 18.
Since the war began, more than 56,000 people have been killed and 132,000 injured, according to the health ministry.
The Israel-Hamas war started following the Hamas-led attack in southern Israel on October 7, 2023, when some 1200 people were killed and around 250 taken hostage.
About 50 of them still remain in captivity in Gaza.
The latest deaths include six people killed and 10 wounded in Israeli strikes on a group of citizens near the Martyrs Roundabout in the Bureij Camp in central Gaza Strip, officials at Awda Hospital in Nuseirat said on Friday.
The United Nations chief, meanwhile, urged leaders to show "political courage" and agree to a ceasefire like the one forged between Israel and Iran.
Secretary-General Antonio Guterres also urged a return to the UN's long-tested distribution system for aid in Gaza, where he said Israeli military operations have created "a humanitarian crisis of horrific proportions".
"The search for food must never be a death sentence," Guterres told reporters.
