The Israeli army on Monday issued a new evacuation order for parts of Khan Yunis and Rafah in southern Gaza, with witnesses reporting that many were fleeing.
Hundreds of thousands had already left Rafah ahead of and during a ground offensive launched by Israeli troops on the southernmost city since early May.
The warning for Al-Qarara, Bani Suhaila and other towns in the two governorates, made on social media and in an official statement, came hours after Israel said 20 "projectiles" were fired into Israel from the Khan Yunis region.
The armed wing of the Palestinian militant group Islamic Jihad claimed the attack. Israel had already staged air strikes in Rafah on Monday.
"Fear and extreme anxiety have gripped people after the evacuation order," said Bani Suhaila resident Ahmad Najjar. "There is a large displacement of residents."
UN Secretary-General Antonio Guterres's spokesman said, "It just shows yet again, that no place is safe in Gaza, more efforts need to be made to protect civilians."
"It's another stop in this deadly circle of movement that the population in Gaza has to undergo on a regular basis," added the spokesman, Stephane Dujarric.
Since launching its ground offensive in Gaza on 7 October, Israeli forces progressively moved south in the Palestinian territory, claiming to destroy Hamas battalions, though fighting has restarted in the north.
Israel's offensive has killed at least 37,900 people, also mostly civilians, according to data from the Gaza Health Ministry.