Israel extended its evacuation warning to cover most of Gaza's main city on Monday and intense fighting erupted.
Israel has now issued three evacuation orders for Gaza City and one for the south of the Palestinian territory since June 27 in a new stepping up of its military operations. The UN says tens of thousands of civilians have fled.
Gaza City residents reported "explosions and numerous gun battles" and helicopter strikes through the night in southwestern neighbourhoods.
Residents said civilians were still leaving the city and many of the displaced said they had already moved from one evacuation zone only to find their new place of refuge had become a target too.
The UN Human Rights Office said it was "appalled" at new orders to civilians, "many of whom have been forcibly displaced multiple times, to evacuate to areas where IDF military operations are ongoing and where civilians continue to be killed and injured".
The office said civilians told to head west out of central Gaza City on Monday were caught up in new fighting as the Israeli army "intensified its strikes in the south and west of Gaza City, targeting the very areas where they had instructed people to move to".
Gaza City residents have now been told to move to the central district of Deir al-Balah, which the UN office said "is already seriously overcrowded with Palestinians displaced from other areas of the Gaza Strip".
The Israeli military said it was pursuing a "counterterrorism operation" against Hamas and Islamic Jihad targets in Gaza City.
"Over the last day, the troops eliminated dozens of terrorists in close-quarters combat and aerial strikes," the military said in a statement, adding that weapons have been seized and an "underground route" destroyed.
