More than 50 Palestinians and an Israeli have died in recent days
Medical staff said four children aged nine to 16 were among the dead, as well as at least six Palestinian militants.
Five Israeli troops were lightly injured in clashes with gunmen inside Gaza, after tanks entered three areas in the north of the territory.
The raids came as Israel said it might launch a full-scale attack on Gaza in response to militant rocket attacks.
The BBC's Katya Adler in Jerusalem says Israel's leaders have been under pressure from some quarters to launch a ground invasion.
However, a recent opinion poll has indicated a majority of Israelis favour a truce with the Islamist movement Hamas, which controls Gaza.
Gaza's citizens were kept awake for another night by the sounds of Israeli military aircraft and missile strikes.
On one occasion, a house east of the Jabaliya refugee camp was struck - two children, a brother and sister, were killed.
Two more civilians, a father and his 19-year-old son, died in an airstrike outside their home.
Later, a 15-year-old girl and her 16-year-old sister were also killed.
Israel says its aim is to stop Palestinian militants firing rockets across the border.
But several more were launched in recent hours, three hitting the Israeli coastal city of Ashkelon and causing light injuries to four people.
On Thursday a rocket fired by Hamas killed an Israeli student in the southern town of Sderot, the first such death in nine months.
Palestinian militant leaders say they are responding to Israeli attacks.More than 50 Palestinians and one Israeli have been killed in the violence since Wednesday.