Twenty-seven people were killed in southern Gaza on Tuesday as Israeli troops opened fire near a US-backed aid centre.
UN chief Antonio Guterres decried the deaths of Palestinians seeking food aid as "unacceptable" and the UN rights chief condemned attacks on civilians as "a war crime", after a similar shooting near the same site on Sunday.
Gaza's civil defence agency said that "27 people were killed and more than 90 injured in the massacre targeting civilians who were waiting for American aid in the Al-Alam area of Rafah", in the territory's south.
Civil defence spokesman Mahmud Bassal earlier told AFP the deaths occurred "when Israeli forces opened fire with tanks and drones".
The International Committee of the Red Cross gave the same death toll but without mentioning the Israeli forces.
The organisation said Gazans face an "unprecedented scale and frequency of recent mass casualty incidents".
The latest shooting occurred about a kilometre from a centre run by the US-backed Gaza Humanitarian Foundation (GHF), which Israel has worked with to implement a new aid distribution mechanism.
The UN and major aid groups have refused to co-operate with the group over concerns it was designed to cater to Israeli military objectives.
At a hospital in southern Gaza, the family of Reem al-Akhras, who was killed in the shooting at Rafah's the Al-Alam roundabout, were beside themselves with grief.
"She went to bring us some food, and this is what happened to her," her son Zain Zidan said.
Akhras's husband, Mohamed Zidan, said "every day, unarmed people" were being killed.
"This is not humanitarian aid; it's a trap."
Rania al-Astal, 30, said she had gone to Al-Alam with her husband to try to get food.
"The shooting began intermittently around 5am. Every time people approached Al-Alam roundabout, they were fired upon," she told AFP.
"But people didn't care and rushed forward all at once — that's when the army began firing heavily." Fellow witness Mohammed al-Shaer, 44, said at first "the Israeli army fired shots into the air, then began shooting directly at the people".
GHF said the operations at its site went ahead safely Tuesday.
UN chief Guterres urged an independent investigation into Sunday's shooting, with his spokesman on Tuesday saying it was "unacceptable civilians are risking and in several instances losing their lives just trying to get food".
The world body's human rights chief Volker Turk called such attacks "unconscionable".
"Attacks directed against civilians constitute a grave breach of international law and a war crime," he said.
The White House said it was "looking into the veracity" of the reports from Rafah.
The health ministry in Gaza said at least 4,240 people have been killed since Israel resumed its offensive on March 18, taking the war's overall toll to 54,510, mostly civilians.