The White House said Wednesday that Israel has so far been taking more "targeted" action in Rafah but renewed its warning to avoid "a lot of death and destruction" in the southern Gaza city.
President Joe Biden earlier this month warned Israel he would stop supplying some arms -- and his administration halted one shipment including massive bombs -- after he voiced opposition to a major assault on Rafah, where more than one million displaced Palestinians had found shelter.
Jake Sullivan, Biden's national security advisor, said he was told during a visit this week to Israel of "refinements" in its plans for Rafah that would allow it "to achieve its military objectives while taking account of civilian harm."
"What we have seen so far in terms of Israel's military operations in that area has been more targeted and limited, has not involved major military operations into the heart of dense urban areas," Sullivan told reporters, Reuters reported.
But he stopped short of saying that Israel had addressed US concerns, adding that Washington was closely watching ongoing Israeli actions.
"There's no mathematical formula. What we're going to be looking at is whether there is a lot of death and destruction from this operation, or if it is more precise and proportional," he said.
"We will see what will unfold."
During a congressional hearing featuring testimony from Secretary of State Antony Blinken, Representative Sara Jacobs praised fellow Democrat Biden for his "red line" on Rafah but said the public might not understand where the line was.