Thousands of Palestinians are fleeing northern parts of Gaza after Israel warned it was targeting the area in its campaign to stop rocket attacks.
The UN says 17,000 people have sought refuge in its facilities as Israeli air strikes continue for a sixth day.
Israeli forces have raided a suspected rocket-launching site in Gaza in their first reported ground incursion.
At least 172 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.
Sirens sounded across the country from first light, as rockets from Gaza continued to hit Israel, but the country's sophisticated Iron Dome missile defence system intercepted the most dangerous.
Six days into this conflict there has not been a single Israeli death from a Hamas rocket.
Despite the growing number of civilian casualties in Gaza, in Israel more than 90% of Israelis support the air campaign. Israel's tanks stand ready to invade Gaza but there is no widespread support for a ground offensive. That, for now, may be all that is stopping this conflict from escalating.
For much of the night, the wounded and the dead were brought into Shifa, Gaza's main hospital.
It was the most sustained bombing so far. For Israel, with US support, it is self-defence but as more Palestinian civilians die, the pressure for a ceasefire is growing.
Israel is not trying to win friends in the Gaza Strip: it does want to weaken Hamas as an organisation. But every time Palestinian civilians die, Hamas gets a popularity boost.
Israel says Hamas attacks its people and is therefore responsible for Palestinian civilian deaths when Israel retaliates, but no Palestinian will listen to that.
At times like this in Gaza, life and death are overshadowed by one reality: almost 70 years of conflict with Israel and no prospect of an end.
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.
UN Relief and Works Agency spokesman Chris Gunness said in a tweet that the agency had doubled its spaces for displaced people from 10,000 to 20,000.
Meanwhile, about 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.
"There are no shelters, no bunkers, no place to go, except their homes," he said. "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.
Israel has been building up its troops along the border with northern Gaza, fuelling speculation of a possible ground invasion.
Defending Israel's actions, Prime Minister Benjamin Netanyahu told US broadcaster CBS: "We're sorry for any accidental civilian deaths but it's the Hamas that bears complete responsibility for such civilian casualties."
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.
At least three Israelis have been seriously injured since the violence erupted, but no Israelis have been killed by the attacks.
A Palestinian health ministry spokesman has said 1,260 people have been injured in Gaza.
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 and the suspected revenge killing of a Palestinian teenager in Jerusalem.
Israel and militants in Gaza fought an eight-day war in November 2012, which ended with a truce.