8 July-2014, BBC: Israel says it hit “40 terror sites” on Tuesday. Palestinian officials say 11 people were killed.
Meanwhile, some 100 rockets have been fired at Israel by militants in Gaza.
Palestinian President Mahmoud Abbas has demanded that Israel end its military campaign.
Israel should “immediately stop its escalation and the raids on Gaza”, Mr Abbas said in a statement published by the official Wafa news agency.
Israel says it will pursue its offensive until rocket fire stops, warning a ground operation has not been ruled out.
“We have to be prepared for that option,” Israeli military spokesman Lt Col Peter Lerner told the BBC.
“We have to be prepared for that escalation. And indeed we are preparing. We have called up some reservists and we are taking the necessary steps around the Gaza Strip to be prepared for that option.”
‘Hamas’ homes hit
Palestinian medics said at least three people were killed in an air strike on a car in Gaza City on Tuesday, the BBC’s Hamada Abuqammar reports.
An Israeli military spokesman said: “We can’t confirm number of casualties, but we can say that hits were identified.”
Another person died at a refugee camp in central Gaza, the health ministry said, while initial reports suggested that at least seven people were killed when a missile hit a house in the southern city of Khan Younis.
The Israeli military said the houses that had been targeted belonged to Hamas members involved in launching rockets or other militant activity, and that they had been used as operations rooms.
Overnight strikes on facilities in Gaza left at least 15 Palestinians injured, Palestinian medical sources said. There have been no reports of Israeli casualties.
After a brief lull, militants continued to fire rockets at cities and towns in southern Israel on Tuesday, including Ashdod and Ashkelon.
Israel says its operation, dubbed Protective Edge, will be expanded in the coming days and that 1,500 reservists have been called up.
At the scene: Yolande Knell, BBC News, Beit Lahiya, Gaza Strip
There have been several loud thuds in the northern Gaza Strip in the past hour as Israeli military planes hit targets here.
The biggest strikes shake the ground and send up huge plumes of smoke.
A woman ran past us with three small children – all were crying and in shock. Nearby a house had just been damaged by an Israeli air strike. Two ambulances whizzed by carrying away the injured.
“[Militants] used to launch rockets from here. [The Israeli military] targeted these houses several times,” a local man told us.
It is extremely tense on the streets and most residents – observing the dawn-to-dusk fast for the Islamic holy month of Ramadan – are staying in their homes.
At the scene: BBC News, Sderot, Israel
Outside a bomb shelter, we heard a loud, dull boom. A small crowd squinted and pointed to a puff of white smoke in the sky.
“It’s an interception,” said one man, suggesting that Israel’s Iron Dome missile defence system had knocked a Hamas rocket out of the sky.
“I’m not happy,” said another man, “because even if there’s an interception, debris still falls.”
At the time of the explosion, Israel’s President-elect, Reuben Rivlin, was inside the underground shelter, giving a briefing.
“Is Israel preparing for war with Hamas?” I asked him.
“We are in war with Hamas because Hamas has declared war on us,” he replied. “We are in war – not because of us – because of Hamas.”
A little later, Mr Rivlin visited schoolchildren, taking summer classes in a fortified classroom which looked like a bunker.
“We have to hit Hamas hard,” said a rabbi.
On the roof of the religious school across the road, a group of students looked out towards Gaza in the distance.
The sudden escalation comes just days after talk of a possible truce between Israel and militant groups in Gaza, with each side suggesting that calm would be answered with calm.
Tensions spiked last week with the murders of three young Israelis in the occupied West Bank and a Palestinian teenager in Jerusalem.
Israel says Hamas was behind the abduction and murder of the Israeli youths – a claim it denies.
A day after their funerals, the Palestinian was abducted in East Jerusalem and murdered. Police have arrested six Jewish suspects and say it seems the 16 year old was killed because of his nationality.
In southern Israel, towns within 40km (24 miles) of Gaza have been instructed by the authorities to close schools and summer camps because of the threat of rocket-fire.
Hamas militants reportedly warned they would enlarge the radius of their targets if Israel continued its air strikes.