"These threats made it impossible to proceed today without putting innocent lives at risk," the organisation said in a statement on Saturday.
"GHF will not be deterred. We remain committed to safe, secure and independent aid delivery. We are actively adapting our operations to overcome these threats and fully intend to resume distributions without delay."
The Israeli military on Saturday retrieved the body of a Thai hostage who had been held in the Gaza Strip since Hamas' October 7, 2023 attack, Defence Minister Israel Katz said, as Israeli airstrikes killed 45 people, according to local medics.
Nattapong Pinta's body was held by a Palestinian militant group called the Mujahedeen Brigades, and was recovered from the area of Rafah in south of the enclave, Katz said.
His family in Thailand has been notified.
Pinta, an agricultural worker, was abducted from Kibbutz Nir Oz, a small Israeli community near the Gaza Strip border where a quarter of the population was killed or taken hostage during the Hamas attack that triggered the devastating war.
Israel's military said Pinta had been abducted alive and killed by his captors, who had also killed and taken to the Gaza Strip the bodies of two more US-Israeli hostages that were retrieved earlier this week.
There was no immediate comment from the Mujahedeen Brigades, who have previously denied killing their captives, or from Hamas.
The Israeli military said the Brigades were still holding the body of another foreigner.
Only 20 of the 55 remaining hostages are believed to still be alive.
The Mujahedeen Brigades also held and killed Israeli hostage Shiri Bibas and her two young sons, according to Israeli authorities.
Their bodies were returned during a two-month ceasefire, which collapsed in March after the two sides could not agree on terms for extending it to a second phase.
Israel has since expanded its offensive across the Gaza Strip as US., Qatari and Egyptian-led efforts to secure another ceasefire have faltered.
Medics in the Gaza Strip said 45 people in total were killed in Israeli air strikes across the enclave on Saturday.
At least 15 Palestinians were killed and 50 wounded by air strikes in the Gaza City district of Sabra in the northern Gaza Strip on Saturday, local health authorities said.
More than one missile landed in the area.
The target seemed to have been a multi-floor residential building but the explosion damaged several other houses nearby, according to witnesses and media.
The Israeli military did not immediately comment.
It later warned people to leave the nearby district of Jabalia, saying it was going to strike there after rockets were launched by militants in the vicinity.
The Palestinian Health Ministry said on Saturday that Gaza's hospitals only had fuel for three more days and that Israel was denying access for international relief agencies to areas where fuel storages designated for hospitals are located.
There was no immediate response from the Israeli military or COGAT, the Israeli defence agency that co-ordinates humanitarian matters with the Palestinian side.
The United Nations has warned that most of Gaza's 2.3 million population is at risk of famine after an 11-week Israeli blockade of the enclave, with the rate of young children suffering from acute malnutrition nearly tripling.
The war erupted after Hamas-led militants took 251 hostages and killed 1200 people, most of them civilians, in the October 7, 2023 attack, Israel's single deadliest day.
Israel's military campaign has since killed more than 54,000 Palestinians, most of them civilians, according to health authorities in Hamas-run Gaza, and flattened much of the coastal enclave.
Families of remaining hostages fear that those alive are in danger from the continued Israeli offensive and those dead will be lost forever.
Israel says the campaign is aimed at bringing them all back and ending Hamas rule in the enclave.
