"It is unacceptable that Palestinians are risking their lives for food," Antonio Guterres said in a statement.

British Prime Minister Keir Starmer said on Monday that the situation in Gaza was getting "worse by the day" and that it was important to ensure the Palestinian enclave receives more humanitarian aid urgently.

"The situation is intolerable in Gaza, and getting worse by the day," Starmer told reporters in Scotland, when asked whether the UK would take any action over the issue.

"Which is why we are working with allies ... to be absolutely clear that humanitarian aid needs to get in at speed and at volumes that it is not getting in at the moment, causing absolute devastation," he added.

Israeli fire killed at least three Palestinians and wounded dozens of others near an aid distribution site operated by the US-based Gaza Humanitarian Foundation, local health authorities said on Monday.

The Israeli military said it was aware of reports of casualties and the incident was being thoroughly looked into.

Earlier on Sunday, Gaza's civil defence agency said Israeli gunfire killed at least 31 Palestinians near a US-backed aid distribution site, with both the group in charge of the site and the military denying any such incident took place.

Israel has faced growing condemnation over the humanitarian crisis in the war-ravaged Gaza Strip, where the United Nations has warned the entire population faces the risk of famine after no aid was allowed to enter for more than two months.

Israel recently eased its blockade and introduced a revamped aid mechanism in cooperation with a newly formed US-backed organisation, bypassing the longstanding UN-led system.

The organisation, the Gaza Humanitarian Foundation (GHF), says it has distributed millions of meals since operations began last week, but the rollout has been marked by chaotic scenes at the limited number of distribution centres.

Civil defence spokesman Mahmud Bassal told AFP that "31 people were killed and more than 176 injured... after Israeli gunfire targeted thousands of civilians near the American aid centre in Rafah", in southern Gaza.

AFP images showed Palestinians transporting bodies on donkey carts near the aid point as others carried away boxes and bags of supplies under the early-morning sun.

Abdullah Barbakh, a 58-year-old Palestinian man, described "chaos" at the site.

"The army opened fire from drones and tanks," he said. "I don't understand why they call people to the aid centres and then open fire on them."

Near another GHF aid centre in central Gaza, AFP images showed rescuers evacuating injured people. Bassal reported one dead and dozens wounded there, again blaming Israeli fire.

The Israeli military said an initial inquiry found its troops "did not fire at civilians while they were near or within the humanitarian aid distribution site and that reports to this effect are false".

"Hamas does everything in its power to undermine food distribution efforts in the Gaza Strip," it added, urging the media to "be cautious with information published" by the group.

A GHF spokesperson also denied any deaths or injuries took place, adding that "these fake reports have been actively fomented by Hamas".