Displaced Palestinians flee Rafah with their belongings to safer areas in the southern Gaza Strip in May 2024 following an evacuation order by the Israeli army the previous day. AFP
The two US officials said Biden does not see the current Israeli operation as "a breaking point" in relations with Israel, Axios said.
"But they warned that if it broadens or gets out of control and Israeli forces go into the city of Rafah itself, it will be a breaking point," it added.
One official said Biden is approaching this the same way he approached the Israeli attack against Iran's retaliation, "pressing Israel not to do it, then accepting something limited."
"If this is all they are going to do we can absorb that, but there is a lot of nervousness about what's next," the official said.
Biden had earlier raised concerns about an Israeli operation in Rafah and said Israel should present a credible and implementable plan for protecting civilians there.
In an interview in March, he was asked whether an Israeli military operation in Rafah was a red line for the administration. "Yes it is," Biden replied.
During a phone call on Monday, Biden warned Israeli Prime Minister Benjamin Netanyahu against launching an offensive in Rafah.
However, "Biden didn't pull the hand break on the capture of the Rafah crossing during the call," a senior Israeli official told Axios.
White House spokesman John Kirby said in a briefing with reporters on Tuesday that Biden's message to Netanyahu during the call was focused on his opposition to a major ground operation in Rafah that would put many civilian lives at risk.
He said Israel told the US that the operation in the Rafah crossing is limited in scope and time and is aimed at preventing Hamas from smuggling weapons through the border.
"They didn't describe it as a major ground operation," Kirby said.
He added that Biden stressed in his call with Netanyahu that the US will follow the operation to see that this is the case.
US Secretary of State Antony Blinken told Israeli Prime Minister Benjamin Netanyahu last week that "a major operation" in Rafah will harm US-Israeli relations.
And the Biden administration last week put a hold on a shipment of US-made ammunition to Israel, a senior US administration official told AP on Tuesday.
The shipment was supposed to consist of 1,800 2,000-pound (900-kilogram) bombs and 1,700 500-pound (225-kilogram) bombs, according to the official, who spoke on a condition of anonymity, with the focus of US concern being the larger explosives and how they could be used in a dense urban setting. More than 1 million civilians are sheltering in Rafah after evacuating other parts of Gaza.
Short link: