At least 60 people have been killed in Israeli strikes across Gaza in a 24-hour period, the territory’s civil defence agency has said, as Israel intensifies its military offensive despite aid agencies warning that the Palestinian population is plunging deeper into malnutrition and famine.

The dead included 10 people in the southern city of Khan Younis, four in the central town of Deir al-Balah and nine in the Jabaliya refugee camp in the north, according to the Nasser, al-Aqsa and al-Ahli hospitals where the bodies were brought..

The strikes that lasted into Friday morning came a day after Israeli tanks and drones attacked a hospital in northern Gaza, igniting fires and causing extensive damage, Palestinian hospital officials said. Videos taken by a health official at al-Awda hospital showed walls blown away and thick black smoke billowing from the wreckage.

The Israeli army said that its forces had attacked “military compounds, weapons storage facilities and sniper posts” in Gaza. “In addition, the [air force] struck over 75 terror targets throughout the Gaza Strip.”

The Palestinian Red Crescent and UN agencies are warning of famine after more than three months of an Israeli blockade on humanitarian aid.

“In the last couple of days we lost 29 children,” the West Bank-based Palestinian Authority health minister, Maged Abu Ramadan, told reporters, describing them as “starvation-related deaths”. He later clarified that the total included elderly people as well as children.

The Palestinian Authority has partial control over the West Bank, which has been occupied by Israel since 1967, but Hamas has ruled the Gaza Strip since 2007.

Food aid is expected to start reaching Palestinians in Gaza this week after Israel began allowing limited goods through after nearly 11 weeks of global pressure to lift the blockade.

Even the US, a staunch ally of Israel, has voiced concerns over the hunger crisis.

A total of 107 aid trucks belonging to the UN and other aid groups carrying flour, food, medical equipment and pharmaceuticals were transferred on Thursday into the strip, the Israeli military said on Friday.

The UN secretary-general, António Guterres, on Friday said Israel has only authorised for Gaza what “amounts to a teaspoon of aid when a flood of assistance is required” to ease the crisis. “Without rapid, reliable, safe and sustained aid access, more people will die – and the long-term consequences on the entire population will be profound,” Guterres told reporters.

“The entire population of Gaza is facing the risk of famine,” Guterres said, adding: “The Israeli military offensive is intensifying with atrocious levels of death and destruction.”

According to UN officials medical supplies were beginning to run low with more than 40% of essential medicines no longer available and rationing of bandages, gloves and similar items.

The greatest shortages were of treatments for skin diseases, which is increasingly prevalent owing to the harsh and unsanitary conditions, and eye drops, internal documents seen by the Guardian show. Reactive agents for some diagnostic tests are also becoming scarce, doctors working in Gaza said.

Aid has yet to reach the vast proportion of the territory’s population, though some has now been distributed to free bakeries in southern regions.

Officials are trying to negotiate with Israeli officials to allow convoys to cross the Netzarim corridor, which bisects the territory, to reach northern Gaza.

“Nothing has changed yet. Some bakeries have been supplied in the middle area and south but it is nothing compared with the needs. People are very, very hungry,” said Amjad Shawa, the director of the Gaza NGOs network.

A World Food Programme convoy was attacked by looters on Thursday night and 15 of 20 trucks loaded with wheat flour hijacked and driven away. Two other trucks broke down.

Aid officials said the threat of looting would continue to seriously hamper aid distribution, as it did before the ceasefire in January. In November, more than 100 trucks of aid were stolen in a single night.

“People are talking a lot about getting baby food in but any child suffering malnutrition needs to be treated properly, and that is relatively straightforward but needs functioning health facilities and we don’t have them at the moment,” said one UN official working in Gaza.

Israel imposed the blockade on all supplies in March, saying Hamas was seizing deliveries for its fighters – a charge the group denies.

The Israeli prime minister, Benjamin Netanyahu, who vowed that the entire Gaza Strip would be under Israeli security control by the end of the war, said his plans for private US companies to deliver aid would prevent a humanitarian crisis, despite aid agencies and many governments saying such a crisis already exists.

Related: Israel still blocking aid for Gaza despite promise to lift siege, says UN

Meanwhile, in Israel, Netanyahu’s decision to appoint the Israel Defense Forces’ Maj Gen David Zini to lead the domestic intelligence agency, Shin Bet – after months of legal and political wrangling over his attempt to sack Ronen Bar from the role – has drawn threats of a legal challenge.

Netanyahu said on Friday his pick for the next domestic intelligence chief would take office ‘‘without delay next month’’.

Bar, who was sacked by Netanyahu in March because of an “ongoing lack of trust”, had been investigating the prime minister’s close aides for alleged breaches of national security, including claims of leaking classified documents to foreign media and allegedly taking money from Qatar, which is known to have given significant financial aid to Hamas.

On Wednesday, Israel’s supreme court ruled as unlawful the government’s decision in March to fire Bar, a move that had triggered mass protests in the country.

With reporting by AP, AFP and Reuters