The White House said Tuesday it was hopeful Israel and Hamas could "close the remaining gaps" in their ceasefire talks, adding that Israel said its military operation in Gaza's Rafah was limited in scope.

"A close assessment of the two sides' positions suggests that they should be able to close the remaining gaps, and we're going to do everything we can to support that process," National Security Council spokesman John Kirby said.

Kirby said the fact that Israel, Hamas's mediator Qatar and CIA chief Bill Burns were all going to be present at the talks in Cairo indicated the talks were at an advanced stage.

"Everybody's coming to the table," the spokesman said in a call with reporters. "That's not insignificant."

Asked what the assessment was based on, Kirby said that "there were amendments offered" and "it's based on our understanding of where the text is right now."

The White House hoped for news "very very soon" but it would be "foolhardy" to predict when the negotiations might bear fruit, he added.

Israel had meanwhile spoken to Washington about its military operation in Rafah in southern Gaza, after sending tanks across the border and seizing control of the main crossing with Egypt.

The military's thrust into the eastern sector of the city packed with displaced civilians came shortly after Hamas said it had accepted a ceasefire proposal, but Israel demurred.

"What we've been told by our Israeli counterparts is that this operation last night was limited and designed to cut off Hamas's ability to smuggle weapons" into Gaza," according to Kirby.

The Israeli operation was of "limited scope, scale, and duration", he added.