Israel says it has warned residents in northern Gaza to evacuate as it prepares to launch fresh air strikes.
Israeli forces have raided a suspected rocket-launching site in Gaza in their first reported ground incursion since operations began on 8 July.
The military says it will continue its offensive until Palestinian militants stop firing rockets at Israeli cities.
At least 159 Palestinians have been killed since Israel's offensive began, according to health officials in Gaza.
The dead are said to include 17 members of one family who died in an Israeli missile strike on Saturday evening.
Israel says it is targeting Hamas militants and "terror sites", including the homes of senior operatives. However, the United Nations has estimated that 77% of the people killed in Gaza have been civilians.
The UN Security Council called for a ceasefire and peace talks on Saturday.
The military confirmed it had dropped leaflets over the city of Beit Lahiya on Sunday morning telling civilians to seek shelter.
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Manuel HassassianPalestinian Authority envoy in UKThere are no shelters, no bunkers, no place to go, except their homes”
"We do not wish to harm civilians in Gaza, but these civilians must know that remaining in close proximity to Hamas terrorists and infrastructures is extremely unsafe," the IDF said.
By 10:30 (07:30 GMT), more than 4,000 Gaza residents had taken refuge at eight bases of the UN Relief and Works Agency, spokesman Chris Gunness said.
Meanwhile, around 800 Palestinians holding dual citizenship began leaving Gaza via Israel's Erez Crossing.
The Palestinian Authority's envoy in the UK, Manuel Hassassian, told BBC News there was nowhere for Gaza residents to hide.
"Hamas is an integral part of the population, and they are resisting from everywhere," he said.
"When Israel says, 'We dropped leaflets to evacuate the northern part of Gaza... we don't need collateral damage' - well, they have been bombarding all of Gaza. And where do these people have to go? There are no shelters, no bunkers, no place to go, except their homes. If they leave their homes, they will be hit on the street."
Early on Sunday, Israeli air strikes destroyed most of the security headquarters and police stations run by Hamas Islamist militants.
The homes next to the compound suffered extensive damage, as they are located in the densely populated neighbourhood of Tel al-Hawa in south Gaza, correspondents say.
The Israel Defense Forces (IDF) said its troops had also raided a site used to fire long-range rockets at Israel.