This was said by Israeli Prime Minister Benjamin Netanyahu, adding that an absolute victory over Hamas could be achieved a few weeks after the offensive begins.
Netanyahu confirmed to CBS on Sunday that talks on a weeks-long ceasefire and the release of the hostages were ongoing, without giving further details.
"We do not believe that an operation, a major military operation, should continue in Rafah unless there is a clear and enforceable plan to protect these civilians, to move them to safe places, feed them, train them and house them," the White House adviser Sullivan told national security, reported Reuters.
Netanyahu wants to completely destroy Hamas, which many call unrealistic.
According to the newspaper, US Secret Service officials said in private conversations with members of the US Congress this week that the Israeli military has killed fewer Hamas fighters than Netanyahu claims, estimating that only about a third are armed members of the movement.
It is likely to rise further as soldiers seek medical attention for symptoms related to traumatic brain injury, two US officials said.
They told CNN that the combat drone exploded near the premises where the American soldiers were housed.
US President Joseph Biden said the attack was carried out by "radical militant groups supported by Iran".