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.
— i.s.t. (@iremsenaa) July 9, 2014
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.
'NOWHERE TO GO'
The military confirmed it had dropped leaflets over the city of Beit Lahiya on Sunday morning telling civilians to seek shelter.
"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.
Four soldiers were lightly injured, it said.
It is believed to be the first time Israeli troops - thought to be naval commandos on this occasion - have entered Gaza since Israel launched Operation Protective Edge.
Israel has been building up its troops along the border with northern Gaza, fuelling speculation of a possible ground invasion.
"We don't know when the operation will end," Israeli Prime Minister Benjamin Netanyahu told a cabinet meeting Sunday. "It might take a long time."
CALL FOR RESTRAINT
The IDF says it has so far struck some 1,320 "terror" sites across Gaza, while Hamas has launched more than 800 rockets at Israel.
Israel's Iron Dome missile shield intercepted several rockets on Sunday above central and southern Israel, Israeli newspaper Haaretz reports.
At least three Israelis have been seriously injured since the violence erupted, but no Israelis have been killed by the attacks.
Palestinian sources say more than 1,000 people have been injured.
France on Sunday again condemned the Hamas rocket attacks, but also called on Israel to "show restraint" in its Gaza campaign and avoid civilian casualties.
Germany is sending Foreign Minister Frank-Walter Steinmeier to Israel on Monday for talks with Israelis and Palestinians to help negotiate an end to the violence.
Rocket fire and air strikes increased after the abduction and killing of three Israeli teenagers in June, which Israel blamed on Hamas and which led to a crackdown on the group in the West Bank. Hamas denied being behind the killings.
Tensions rose further after the suspected revenge killing of a Palestinian teenager in Jerusalem on 2 July. Six Jewish suspects were arrested over the youth's abduction and murder.
Israel and militants in Gaza fought an eight-day war in November 2012, which ended with a truce.