The US has written to Israel, giving it 30 days to boost humanitarian aid access in Gaza or risk having some US military assistance cut off.

The letter, sent on Sunday, amounts to the strongest known written warning from the US to its ally and comes amid a new Israeli offensive in northern Gaza that has reportedly caused a large number of civilian casualties.

It says the US has deep concerns about the deteriorating humanitarian situation, adding that Israel denied or impeded nearly 90% of humanitarian movements between the north and south last month.

Israel is reviewing the letter, an Israeli official was reported as saying, adding the country “takes this matter seriously” and intends to “address the concerns raised” with US counterparts.

Israel has previously said it is targeting Hamas operatives in the north and not stopping the entry of humanitarian aid.

The secretaries said Israel denied or impeded about 90 per cent of humanitarian movements between north and south Gaza last month. They were “particularly concerned” that “recent actions by the Israeli government” were “contributing to an accelerated deterioration in the conditions in Gaza”.

On Monday, the Israeli military body responsible for managing crossings into Gaza, Cogat, said 30 lorries carrying aid from the World Food Programme had entered northern Gaza through the Erez crossing.

That ended a two-week period during which the UN said no food aid was delivered to the north, and supplies essential for survival were running out for the 400,000 Palestinians there.

A UN official has said that Gaza is in a state of “constant peak emergency”.

Antoine Renard, head of the World Food Programme (WFP) in the occupied Palestinian territories, told the AFP news agency people in the north of the territory were “relying solely on assistance” with practically no access to fresh food other than that provided by UN agencies.

The US is by far the biggest supplier of arms to Israel, and the Israeli military has relied heavily on US-supplied aircraft, guided bombs, missiles and shells to fight the war against Hamas in Gaza over the past year.

It states that Israeli evacuation orders have forced 1.7 million people into the narrow, coastal al-Mawasi area where they are at “high risk of lethal contagion” due to extreme overcrowding, and that humanitarian organisations report that their survival needs cannot be met.

The letter says Israel “must, starting now and within 30 days” act on a series of concrete measures to boost aid supplies, adding that failure may “have implications for US policy”.

It cites US laws which can prohibit military assistance to countries that impede delivery of US humanitarian aid.

It says Israel must “surge all forms of humanitarian assistance throughout Gaza” before winter, including by enabling a minimum of 350 lorries a day to enter through all four major crossings and a new fifth crossing, as well as allowing people in al-Mawasi to move inland.

It also calls on Israel to end the “isolation of northern Gaza” by reaffirming that there will be “no Israeli government policy of forced evacuation of civilians” from north to south.

At a news conference in Washington on Tuesday, US state department spokesman Matthew Miller told reporters that the letter was “a private diplomatic communication that we did not intend to make public”.

He also said the 30-day time limit was not linked to the upcoming US presidential election on 5 November, saying it was “appropriate to give them time to work through the different issues”.

Israel has previously insisted there are no limits to the amount of aid or humanitarian assistance that can be delivered into and across Gaza, and blames UN agencies for failing to distribute supplies. It also accuses Hamas of stealing aid, which the group denies.