Soldiers carrying out the operation in Shejaia, a suburb east of Gaza City in the north, were letting civilians out via organised routes as troops moved in to expand the area defined by Israel as a security zone, a statement said.
Images circulating on social media showed an Israeli tank on Al Muntar hill in Shejaia, in a position that gave it clear sight over Gaza City and beyond to the shoreline.
Shelling on the eastern side of Gaza was non-stop, a local health official said in a text message.
Where Israeli forces moved in, hundreds of residents had already left a day earlier, carrying belongings or loading them on to vans or donkey carts, after the military issued the latest in a series of evacuation warnings that cover about a third of the Gaza Strip, according to the United Nations.
Israel resumed its operation in the enclave with a heavy series of air strikes on March 18 and sent troops back in after a two-month pause during which 38 hostages were returned in exchange for hundreds of Palestinian prisoners and detainees.
Efforts at restarting negotiations, brokered by Egypt and Qatar, have stalled.
"There are currently no contacts," a Palestinian official close to the mediation effort told Reuters.
Over the past two weeks, more than 280,000 people have been displaced in the Gaza Strip, according to United Nations humanitarian agency OCHA, adding to misery for families already repeatedly displaced over the past 18 months.
"I swear to God that I am staying in the street, there is no shelter here," said 40-year-old Hemam al-Rifi, who said members of his family were killed when the Gaza City school complex they were sheltering in was hit by a deadly strike on Thursday.
"My house was destroyed at first, and I stayed in a tent in a school, not a classroom, and now I don't know where to go."
In Gaza City, local people said Israeli strikes had hit a water desalination plant that was vital in providing clean drinking water.
Aid supplies have been cut off for weeks.
On the southern edge of the Gaza Strip, Israeli troops have been consolidating around the ruins of the city of Rafah and the UN says 65 per cent of the enclave is now within "no go" areas, under active displacement orders, or both.
At least 19 people were killed in the southern city of Khan Younis when a three-storey house was hit by an Israeli strike, the Palestinian news agency WAFA reported.
Numerous people were also injured.
The information could not be independently verified.
Israel's army said it was examining the report.
Israeli ministers have said the operation will continue until 59 hostages still held in the Gaza Strip are returned.
Hamas says it will free them only under a deal that brings a permanent end to the war.
On Friday, a spokesperson for the group's armed wing said half of the hostages were being held in areas where people had been told to leave.
"If the enemy is concerned about the lives of these hostages, it must immediately negotiate their evacuation or release," Abo Ubaida said in a message on Telegram.
The Israeli military said its forces killed Mohammed Awad, a senior commander in the militant group Palestinian Mujahideen, who it said was involved in the abduction of hostages including the Bibas family during the attack on Israel on October 7, 2023 and was most likely involved in their killing.
Israel accuses Hamas of hiding fighters in civilian buildings and says it takes precaution to limit casualties but hundreds of Palestinians have been killed since the operation resumed, according to local health authorities.
More than 250 of the dead were armed militants, the military says.
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 the strip to ruins and killed more than 50,000 Palestinians, according to the enclave's health authorities.
with DPA
