In a call, US President Joe Biden told Mr Netanyahu that Israel should not proceed with a military operation in Rafah without a plan to ensure the safety of people sheltering there, the White House said.
The call came days after Biden said Israel’s response in Gaza was “over the top”.
A senior Biden administration official said negotiators working on a deal to release the remaining hostages held by Hamas had made “real progress” over the last few weeks.
There were still some “significant” gaps to close, the official said, but added: “It’s pretty much there.”
Before previous assaults on Gaza cities, Israel’s military has ordered civilians to leave without preparing any specific evacuation plan. Aid agencies say an assault on Rafah would be catastrophic.
The war began on Oct 7 when the militant group Hamas that controls Gaza stormed the border fence with Israel, sending in fighters who killed 1,200 people, mostly civilians, and seized about 250 hostages, according to Israeli tallies.
Four months later, Gaza is in ruins. Under a massive daily bombardment, Israeli ground forces have overrun most of the enclave, smashing houses, public buildings and infrastructure with air raids, artillery fire and controlled detonations.
Palestinian health authorities say more than 28,000 people have been killed in the war, about 70 per cent of them women and children. More than 85 per cent of Gazans are homeless. A UN survey found that nearly one in 10 children under five are acutely malnourished.
Talks for a deal on a ceasefire and the release of hostages have so far failed to bring an agreement. Last week Israel rejected a Hamas proposal, saying it would not stop fighting while the group retained brigades that Israel says are hiding in Rafah.