Four young girls from the same family and two young boy were among those killed in raids overnight, Palestinian medics said.
Tzipi Livni, the Israeli foreign minister, told the US media that Israel was only targeting Hamas and other armed Palestinian groups.
"Unfortunately in a war ... sometimes also civilians pay the price," she said.
She also told NBC's Meet The Press: "Our goal is not to reoccupy Gaza Strip."
Israeli officials have said that the assault on Gaza was a response to rocket and mortar attacks by Palestinian fighters.
On Monday, at least one civilian was killed when a rocket hit the southern Israeli city of Ashkelon. It was the second such fatality since the offensive was launched.
With hundreds of troops and tanks being deployed along the edge of the territory there were growing fears that the air bombardment could be followed by a ground incursion.
"The indications here on the ground are certainly that the build-up is there, that the preparations are there for a ground offensive," Al Jazeera's Hoda Abdel Hamid, reporting from Izmit in Israel, said.
The Israeli cabinet approved the call-up of 6,500 military reservists and Ehud Barak, Israel's defence minister, has warned that the air raids could be followed by a ground offensive.
"If it's necessary to deploy ground forces to defend our citizens, we will do so," Barak's spokesman quoted him as saying.
Earlier on Sunday, Israeli aircraft bombed the length of the Gaza-Egypt border, taking out tunnels used to smuggle in vital goods to the besieged strip.
Dozens of tunnels are said to criss-cross between southern Gaza and Egypt's Sinai desert, providing a lifeline to residents who are starved of basic supplies due to an 18-month-long Israeli blockade.
Avital Leibovitch, an Israeli army spokeswoman, said: "The air force just attacked over 40 tunnels found on the Gaza side of the border.
"We believe [they] were used for smuggling weapons, explosives and sometimes people," she said. "The pilots notified direct hits on these targets."
Ayman Mohyeldin, Al Jazeera's correspondent in Rafah, a town split in half by the border, said at least one person died and 42 others were injured in the attacks on the tunnels.
"It's certainly a devastating blow to the civilian population in Gaza," he said, adding that speculation the tunnels might be hit had already caused the price of fuel and other goods to soar.
Palestinians attempting to flee the Israeli bombardment managed to breach the border fence with Israel, prompting clashes with security forces during which at least one person was killed.
Tensions at the crossing with Egypt, bypassing Israel, had risen during the day, with Egypt blaming Hamas for not letting wounded Palestinians through and Hamas asking for medical aid to be handed over.
Israel said it began its aerial assault on Gaza in response to rocket attacks launched by Hamas fighters into the south of the country.
A six-month truce between Israel and Hamas in the Gaza Strip ended on December 19.