Deaths continue to mount, with at least 83 people now killed in Gaza and seven in Israel.
A BBC reporter in Gaza said it had been the "longest and most difficult night since the 2014 war". Israel said it had been targeted with 1,600 rockets.
Israel is now mulling a possible ground operation in Gaza.
It has sent reinforcements to the border.
This is now the worst violence since 2014, fuelled initially by weeks of Israeli-Palestinian tension in East Jerusalem which led to clashes at a holy site revered by both Muslims and Jews. This spiralled into an incessant exchange of Palestinian rocket fire and Israeli airstrikes.
The fear among civilians on both sides is taking its toll.
Najwa Sheikh-Ahmad, a Gaza mother, said of Wednesday night: "You cannot sleep... In any moment your home might be your grave.
"You cannot be secure. As a mother it's very terrifying, it's very exhausting for my feelings, for my humanity," she told the BBC's Today programme.
In Israel, an apartment block was destroyed in the city of Petah Tikva shortly after residents had gone to their bomb shelters.
"We heard an alarm and suddenly there was a bang. Smoke entered the shelter, and the neighbour next to me who was sitting on a chair flew back," one resident told the news website Ynet.
Mohammed Abu Rayya, a doctor living in Gaza told the BBC: "[There are] a lot of deaths, a lot of wounded - children, old women and old men. We cannot sleep at home, we are not feeling safe. Air strikes all over Gaza. There are not any places safe."
Authorities in Gaza, which is controlled by the Islamist militant group Hamas, say many civilians have died, including 17 children.
Israel says dozens of those killed in Gaza were militants, and that some of the deaths are from misfired rockets from Gaza.
The Israel Defense Forces (IDF) said they had struck Hamas targets more than 600 times. They said they had targeted homes and businesses used by militants and a school Hamas was using "to hide a terror tunnel".