The launch of the operation came despite fierce opposition from Israel’s key allies. Joe Biden, the US president, urged Mr Netanyahu not to go ahead with the invasion in the hours before news broke of Hamas’s ceasefire offer.

“We’ve made clear our views about operations in Rafah that could potentially put more than a million innocent people at greater risk,” said John Kirby, the White House’s national security spokesman.

“During this call with prime minister Netanyahu, the president again made this clear. He also made clear that we continue to believe that the hostage deal is the best way to avoid that sort of an outcome.”

Mr Kirby added that the White House was examining Hamas’s ceasefire proposal and would soon communicate its views to Qatar, Israel and Egypt. He said Mr Netanyahu had agreed to keep aid flowing into Gaza through Kerem Shalom, the key crossing into the south of the Strip.

Four Israeli soldiers were killed in an attack at the crossing on Sunday, which was claimed by the armed wing of Hamas.

On Monday, Rishi Sunak said he was “deeply concerned” by the prospect of a Rafah offensive, and Sir Keir Starmer, the Labour leader, called for it to be dropped entirely.

Jordan’s King Abdullah, who met Mr Biden in Washington on Monday, said the Israeli attack on Rafah threatened a “new massacre”.