Aid supplies are expected to enter Gaza on Monday after a blockade lasting nearly three months and warnings of famine.
A UN official told the Associated Press news agency that 20 aid trucks carrying mostly food would go into the territory.
Israel's Prime Minister Benjamin Netanyahu agreed to allow limited deliveries to resume after pressure from allies concerned about "images of hunger" which they "cannot accept".
In a video statement, posted to social media on Monday, Mr Netanyahu said Israel's "greatest friends in the world" - which he did not specify - had threatened to withdraw support for his country.
He added that a "starvation crisis" would jeopardise Israel's new offensive against Hamas in Gaza, and a "basic" amount of food would be allowed in.
On Monday, the Israeli military issued an evacuation order for residents of Gaza's second-largest city, Khan Younis, and nearby towns, warning that the entire area "will be considered a dangerous combat zone".
In a news conference on Monday, foreign ministry director general Eden Bar Tal accused Hamas of "hijacking" food and monetising aid "in order to feed its engine of war".
He said a new distribution mechanism would become operational within days, organised by the US-backed group Gaza Humanitarian Foundation (GHF), to "direct aid to the population in Gaza, but not to Hamas".
Mr Tal said Israel would "temporarily bridge the current needs" until GHF's operation begins, beginning on Monday, with trucks loaded with baby food being allowed into Gaza.
"The items to be supplied immediately include flour to the main bakeries operated by international organisations in the Gaza Strip, supplies of items to central kitchens operated by international organisations, baby food and medical supplies."
Meanwhile, international aid groups say they will not participate in the new distribution mechanism, saying it is not practical and won't reach the most vulnerable Palestinians.
Mr Netanyahu said Israel aimed to take control of all of Gaza and prevent Hamas militants from looting aid shipments - something it denies doing.
Israel has just ramped up its offensive in Gaza - where it's been conducting a military campaign in retaliation for 1,200 people killed and 251 taken hostage by Hamas on 7 October 2023.
Gaza's health ministry says more than 53,000 people have died in Israel's 19-month campaign, although it does not distinguish between civilians and combatants. It reported 464 people had died in Israeli military strikes in the week to Sunday
On Sunday, a British surgeon working in Gaza said in a video to Sky News that the enclave is now "a slaughterhouse" amid Israeli bombardment.
Ceasefire talks took place in Qatar over the weekend - with Israel saying they involved discussions with Hamas on ending the war as well as a truce and hostage deal - although there was no breakthrough.
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In a statement on Sunday, IDF said its air force struck "over 670 Hamas terror targets throughout the Gaza Strip to disrupt enemy preparations and support ground operations" over the past week.
Israel previously said it aimed to pressure Hamas, seize territory, displace Palestinians to the south and take greater control over the distribution of aid.
Gaza has been under a complete blockade on humanitarian aid since 2 March.
Global food security experts have warned of famine across the territory, and after recent UN-backed report from warned one in five people in Gaza were facing starvation.
(c) Sky News 2025: Israel to allow 'basic quantity of food' into Gaza, after allies apply pressure on Benjamin Netanyahu