Soldiers carrying out the operation in Shejaia, a suburb east of Gaza City in the north, were letting civilians out via organised routes, the military said on Friday.
Israel issued evacuation warnings in the area on Thursday, and hundreds of residents streamed out, some carrying their belongings as they walked, others on donkey carts and bikes or in vans.
Gaza health authorities said Israeli forces killed at least 27 people, including women and children, in an air strike on a school building in Gaza City where displaced families were sheltering.
The military said the Dar Al-Arqam school building in Tuffah neighbourhood in Gaza City had been used a command and control centre by Hamas militants and accused the fighters of deliberately using civilian infrastructure as bases.
Hamas denies that it operates among civilians.
Hundreds of thousands of Palestinians have been fleeing their homes in recent days in one of the biggest mass exoduses of the war, as Israeli forces have moved to expand the territory under their control.
On the southern edge of Gaza, Israeli troops have been consolidating around the ruins of the city of Rafah.
Israel has not fully explained its long-term aim for the areas it is now seizing as a security zone.
Gaza residents say they believe the aim is to permanently depopulate swathes of land, including some of Gaza's last farmland and water infrastructure.
The military said it had killed numerous militants and dismantled infrastructure, including what it said was a Hamas command and control centre.
Palestinians say Israel's ultimate aim is to displace Gaza's population permanently, in line with a plan announced by US President Donald Trump to turn the enclave into a waterfront resort under US control.
Israel says it would encourage Palestinians who wish to leave voluntarily.
Israeli troops resumed their operation in Gaza on March 18, following a two-month truce.
Ministers have said the operation will continue until 59 hostages still held in Gaza are returned.
Hamas says it will free them only under a deal that brings a permanent end to the war.
The war began when Hamas fighters stormed into Israeli communities on October 7, 2023, killing 1200 people and capturing more than 250 hostages, by Israeli tallies.
Since then, Israel has reduced much of Gaza to ruins and killed more than 50,000 Palestinians, according to the enclave's health authorities.
