Mr Biden warned Mr Netanyahu during a phone call on Sunday that he believes “a military operation in Rafah should not proceed without a credible and executable plan.”
Reports have given an insight into Mr Biden and Mr Netanyahu’s private conversations.
The US President reportedly told the Israeli Prime Minister: “I love you, Bibi, even if I can’t stand you.”
White House sources have claimed that Mr Biden has said Mr Netanyahu is “giving him hell” over the conflict in Gaza.
As reported by the Telegraph, another source said of the President: “He just feels like this is enough. It has to stop.”
Mr Biden even told donors recently that Mr Netanyahu has “been a pain in my a– lately” or “he’s been killing me lately”.
The Telegraph reports that Mr Biden has been urged by his staff to be publicly critical of Israel, and he is said to be coming round to the idea.
This comes after US State Department spokesman Matthew Miller said he does not believe the air strikes carried out during Israel’s rescue mission in Rafah was a “launch of a full-scale offensive.”
He added: “We will make clear – as we did last weekend, as the president did in his conversation over the weekend – that without such a plan that is credible, and that they can execute, we do not support a full-scale military operation there going ahead.”
On the question of aid to Israel being cut, , Mr Miller said: “You’ve got to look… at how such a step would be received by Israel’s opponents, both inside Gaza and outside of the state of Israel.”
A spokesperson for the National Security Council added: “The president has been clear where he disagrees with Prime Minister Netanyahu, but this is a decades-long relationship that is respectful in public and in private.”
