Israeli tanks have seized several districts and advanced west and north of Rafah in recent days.
Israel is yet to accept the three-phase Israeli proposal US President Joe Biden outlined last month.
Parents say they have no choice but to watch their children waste away as Israel’s siege prevents enough food getting into the enclave.
The US State Department calls for a swift investigation into what happened.
Political pressure is building in Israel for tougher action.
Israeli strikes have killed at least 45 Palestinians in Gaza on Saturday.
Residents said the tanks moved into five neighbourhoods shortly after midnight local time.
Both Israel and Hamas committed war crimes in the early stages of the Gaza war, a U.N. inquiry found.
"There are a lot of details to be worked out."
