Gaza's civil defence agency said Israeli gunfire killed at least 31 people and wounded 176 near the aid distribution site in the southern city of Rafah on Sunday, with medics at nearby hospitals also reporting a deluge of gunshot wound victims.
The Israeli military denied firing at people "while they were near or within" the site.
But a military source acknowledged "warning shots were fired towards several suspects" overnight about a kilometre away.
"I am appalled by the reports of Palestinians killed and injured while seeking aid in Gaza yesterday. It is unacceptable that Palestinians are risking their lives for food," Guterres said in a statement.
"I call for an immediate and independent investigation into these events and for perpetrators to be held accountable."
Guterres stressed that the Israeli occupying authorities have clear obligations under international humanitarian law to approve and facilitate humanitarian aid delivery.
He further emphasised the urgent need to restore the large-scale, unimpeded entry of humanitarian aid into the Gaza Strip to meet the immense needs of the population, underscoring the necessity of allowing the United Nations to operate in safety and security with full respect for humanitarian principles.
He reiterated his call for an immediate, durable, and sustained ceasefire in Gaza, along with the unconditional release of all hostages, affirming that this is the only way to ensure security for all and that there is no military solution to this conflict.
Earlier Monday, UNRWA Commissioner-General Philippe Lazzarini warned that the distribution of humanitarian aid in Gaza has turned into what he described as 'a death trap', amid the ongoing Israeli bombardment.
The UN and humanitarian organizations have held the Israeli occupation fully responsible for deliberately obstructing aid access, deeming such actions unconscionable violation of international law and a direct threat to civilian lives.
The Israeli government has worked with the group running the site, the Gaza Humanitarian Foundation (GHF), to introduce a new mechanism for distributing aid in Gaza that has bypassed the longstanding UN-led system.
The UN has declined to work with the group out of concerns about its neutrality.
GHF said that as of Monday, it had distributed more than 5.8mn meals' worth of food from its centres.
Israel has come under increasing international pressure to improve the humanitarian situation in Gaza following a more than two-month blockade on aid that was only recently eased.
The UN has warned the entire population is at risk of famine, and has also reported recent incidents of aid being looted, including by armed individuals.
Talks aimed at reaching a ceasefire have so far failed to produce a breakthrough.
14 killed in strike on Jabalia home; Gaza toll rises to 54,470
Gaza's civil defence agency said an Israeli strike on a home in the northern town of Jabalia killed 14 people Monday."The number of martyrs from the targeting of the Al-Bursh family home has risen to 14, including six children and three women, in addition to more than 20 missing individuals still under the rubble," agency spokesman Mahmud Bassal said.
The toll from the ongoing Israeli aggression on the Gaza Strip reached 54,470 martyrs and 124,693 injuries since October 7, 2023.