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The US has rebuffed an Israeli plan for relocating Palestinians from Gaza's overcrowded southern city of Rafah ahead of a long-threatened ground incursion, an Israeli broadcaster reported on Tuesday.

The IsraeliÌýChannel 12 said US Secretary of State Antony Blinken and other officials spoke on Monday with the head of Israel's National Security Council and Ron Dermer, Tel Aviv's strategic affairs minister.

They talked via video chat about alternative suggestions from the US regarding Israeli army operations in Rafah, where 1.4 million Palestinians are currently seeking shelter amid Israel's devastating war on Gaza.

According toÌýChannel 12,ÌýUS National Security Adviser Jake Sullivan warned over the humanitarian crisis in Gaza.

"You are on the verge of being responsible for a famine crisis in the 21st century, and this is not acceptable," he said.Ìý

"The evacuation plan you have presented so far is neither impressive nor feasible," he added.

Blinken reportedly sarcastically said: "According to the pace of your work in bringing in humanitarian aid, it will take four months to evacuate Rafah."

Many of the Palestinians currently in Rafah were displaced from other parts of Gaza, including the north, since the start of the war on 7 October.

An Israeli minister argued the relocation of Palestinians was necessary to go into Rafah and to "dismantle" Hamas.

Sullivan responded to the comments, saying: "If there is no organised plan for the next day [of the war], then nothing will help you push towards dismantling Hamas, not Rafah and not anything else."

Channel 12 said Israeli officials such as ambassador to the US Michael Herzog were also on the call, as were participants from the US defence department.

A joint statement about the meeting was published by the White House on Monday.

The statement said Israel and the US had a "constructive engagement on Rafah".

"The US side expressed its concerns with various courses of action in Rafah," it added.

"The Israeli side agreed to take these concerns into account and to have follow up discussions between experts, overseen by the SCG [Strategic Consultative Group].

"The follow up discussions would include in person SCG meeting as early as next week."

Israel'sÌýwar on Gaza has so far killed almost 33,000 people and wounded more than 75,500 others, according to the enclave's health ministry.