"This is a difficult and very disappointing statement to hear from a president to whom we have been grateful since the beginning of the war," Israel's ambassador to the United Nations, Gilad Erdan, said on public radio in Israel's first reaction to Biden's warning.

Israel has defied international objections by sending in tanks and conducting "targeted raids" in the eastern areas of Rafah.

It says Rafah is home to Hamas's last remaining battalions but the city on the border with Egypt is also crammed with displaced Palestinian civilians.

"If they go into Rafah, I'm not supplying the weapons that have been used... to deal with the cities," Biden told CNN, in his starkest warning to Israel since the start of the war.

"Civilians have been killed in Gaza as a consequence of those bombs," Biden said. "It's just wrong."

Erdan said Biden's comments would be interpreted by Israel's foes Iran, Hamas, and Hezbollah as "something that gives them hope to succeed".

"If Israel is restricted from entering an area as important and central as Rafah where there are thousands of terrorists, hostages and leaders of Hamas, how exactly are we supposed to achieve our goals?" he said.

"This is not a defensive weapon. This is about certain offensive bombs. In the end the State of Israel will have to do what it thinks needs to be done for the security of its citizens."

Israel's far-right Finance Minister Bezalel Smotrich said his government would pursue its goals in Gaza despite the US threat.

"We will achieve complete victory in this war despite President Biden's push back and arms embargo," he said in a statement.

"We must continue the war until Hamas is totally eliminated and our hostages are back home. This involves conquering Rafah completely and the sooner the better."

AFP journalists reported heavy shelling in Rafah early Thursday, and the Israeli military later said it was also striking "Hamas positions" further north in the centre of the Gaza Strip.

On Tuesday, Israeli forces seized Rafah's border crossing into Egypt, which has served the main entry point for aid into besieged Gaza.