The Israeli prime minister, Benjamin Netanyahu, has rejected Joe Biden’s comment that his approach to the war in Gaza is “hurting Israel more than helping Israel”, escalating a dispute between the leaders.

Over the weekend, the US president said Netanyahu “must pay more attention to the innocent lives being lost as a consequence of the actions taken” in Gaza and that his stance was detrimental to Israel’s interests.

Netanyahu hit back on Sunday night in an interview with Politico. If Biden meant “that I’m pursuing private policies against the majority, the wish of the majority of Israelis, and that this is hurting the interests of Israel, then he’s wrong on both counts”, Netanyahu said.

Biden – who has backed Israel during the five-month-old war with Hamas but whose frustration with Netanyahu has grown increasingly visible – aired his criticism in an interview with MSNBC.

Biden said a potential invasion of Rafah – the last place of relative safety in Gaza – was “a red line” for him, but added that he would never “leave Israel”.

“The defence of Israel is still critical, so there’s no red line I’m going to cut off all weapons so they don’t have the Iron Dome to protect them.”

Netanyahu’s failure to secure the release of hostages still held by Hamas militants, whose 7 October attack on southern Israel triggered the war, has led to regular protests in Israel and calls for early elections, including in Tel Aviv again on Saturday night.

The war in Gaza began with Hamas’s unprecedented attack, which killed about 1,160 people, mostly civilians. Israel’s retaliatory military campaign has, according to Gaza’s Hamas-run health ministry, killed at least 31,045 people in Gaza, mostly women and children.

But Netanyahu said in the interview that this figure included 13,000 militants.

“How do I know that? Because our forces have killed at least 13,000 terrorist fighters,” he said, without elaborating on how that figure was derived.

Hamas has not said how many of its members have been killed in the fighting.

After five months of war, the UN says a quarter of people in Gaza are on the brink of starvation. The local health ministry said on Saturday that 23 people, including several children, had died of dehydration or malnutrition in the previous 10 days.

Aid agencies’ efforts to get humanitarian aid to where it is most needed have been hampered by a combination of logistical obstacles, a breakdown of public order and lengthy requirements imposed by Israel.

The plan to open an EU-backed sea corridor from Cyprus, along with aid airdrops by the US, Jordan and others, reflects a growing frustration among even Israel’s closest allies that it is not doing enough to get aid to Gaza’s civilians. The number of aid trucks entering the territory by land over the past five months has been far below the 500 a day that entered before the war.

Israeli authorities have consistently denied allegations that it has blocked delivery of aid. “Hamas has been stealing humanitarian aid and stockpiling equipment and food for Ramadan for terrorist leaders instead of the Gazan civilians in need,” the Israel Defense Forces spokesperson R Adm Daniel Hagari said on Saturday.

There has been growing pressure on Israel and Hamas to agree to a ceasefire before Ramadan, which starts on Monday. However, no deal has been made.

An aid ship carrying 200 tonnes of food was due to set sail for Gaza from Cyprus over the weekend but was delayed due to “technical difficulties”, according to local media, and was instead expected to set off on Monday. Work had begun on Sunday on a floating jetty in Gaza where the aid could be received, said a spokesperson for one of the organisations responsible for the shipment.

In a separate development, a US military vessel carrying equipment for the construction of a second temporary pier in Gaza was en route to the Mediterranean, officials in Washington said. It could be weeks before the facility was functional, they added.

Speaking to Politico, Netanyahu predicted the fighting could take another four to eight weeks. It would not take than two months, he said: “Maybe six weeks, maybe four.”

Netanyahu said Israelis “say that once we destroy the Hamas, the last thing we should do is put in Gaza, in charge of Gaza, the Palestinian Authority that educates its children towards terrorism and pays for terrorism”.

Netanyahu has drawn global condemnation and defied the US, which provides Israel with billions of dollars in military aid, by rejecting calls for a Palestinian state.

Biden’s secretary of state, Antony Blinken, has spoken of reforming the Palestinian Authority (PA), which has partial administrative authority in the Israeli-occupied West Bank, in a way that could “reunite” it and Gaza under PA leadership.

But Netanyahu said Israelis “also support my position that says that we should resoundingly reject the attempt to ram down our throats a Palestinian state”.