Some 150,000 Gazans have fled from Rafah since the start of the week, fearing an Israeli advance into the city, the United Nations Relief and Works Agency for Palestine Refugees (UNRWA) posted on X on Saturday.
However, the Israel Defense Forces say an estimated 300,000 people had followed the evacuation orders since the beginning of the week, in a statement that could not be independently verified.
Israel has now expanded its calls on residents of Rafah to include those in the centre and other parts of the city, telling them to move to the town of Al-Mawasi on the Mediterranean coast.
The army seems set to expand its operation to eliminate Palestinian militant Islamist Hamas, though calls are growing louder to desist, including from the UN and the United States, Israel's main backer.
Families are packing their belongings all over the city, an UNRWA employee wrote on X. "The streets are much emptier."
UNRWA says 110,000 Palestinians had left the city on the border with Egypt by the previous day.
Some 300,000 people are affected by Israel's latest evacuation orders, which also cover areas in other parts of the coastal strip, UNRWA says.
