Gunfire killed at least a dozen people waiting for aid trucks close to the Zikim crossing with Israel in the north, said staff from Shifa hospital, where bodies were taken.
Israel's military said it fired warning shots to distance a crowd "in response to an immediate threat," and it was not aware of any casualties.
A witness, Sherif Abu Aisha, said people started running when they saw a light that they thought was from aid trucks, but as they got close, they realised it was Israel's tanks.
That's when the army started firing, he told The Associated Press. He said his uncle was among those killed.
"We went because there is no food ... and nothing was distributed," he said.
Elsewhere, those killed in strikes included four people in an apartment building in Gaza City, hospital staff and the ambulance service said.
Another Israeli strike killed at least eight people, including four children, in the crowded tent camp of Muwasi in the city of Khan Younis in the south, according to the Nasser hospital, which received the bodies.
Also in Khan Younis, Israeli forces opened fire and killed at least nine people trying to get aid entering Gaza through the Morag corridor, according to the hospital's morgue records. There was no immediate comment from Israel's military.
Ceasefire talks between Israel and Hamas were at a standstill after the US and Israel recalled negotiating teams on Thursday.
Israeli Prime Minister Benjamin Netanyahu said Friday his government was considering "alternative options" to ceasefire talks.
A Hamas official, however, said negotiations were expected to resume next week and described the recall of the Israeli and US delegations as a pressure tactic.
Egypt and Qatar, which mediate the talks alongside the United States, called the pause only temporary and said talks would resume. They did not say when.
"Our loved ones do not have time for another round of negotiations, and they will not survive another partial deal," said Zahiro Shahar Mor, nephew of hostage Avraham Munder, one of 50 still in Gaza from Hamas' attack on October 7, 2023, that sparked the war. Mor spoke at a weekly rally in Tel Aviv.
The United Nations and experts say Palestinians in Gaza are at risk of famine.
"We only want enough food to end our hunger," said Wael Shaaban at a charity kitchen in Gaza City as he tried to feed his family of six.
Israel on Saturday said over 250 trucks carrying aid from the UN and other organisations entered Gaza this week.
About 600 trucks were entering per day during the latest ceasefire that Israel ended in March.
Israel faces growing international pressure to alleviate Gaza's catastrophic humanitarian crisis.
More than two dozen Western-aligned countries and over 100 charity and human rights groups have called for an end to the war, harshly criticising Israel's blockade and a new aid delivery model it has rolled out.
More than 1000 Palestinians have been killed by Israeli forces since May while trying to get food, mostly near the new aid sites run by an American contractor, the UN human rights office says.
For the first time in months, Israel said it is allowing airdrops, as requested by neighbouring Jordan.
But the head of the United Nations agency for Palestinian refugees, Philippe Lazzarini, warned on social media that airdrops are "expensive, inefficient and can even kill starving civilians".
