Three children were among seven Palestinians killed in Israeli airstrikes on Gaza, while four more four died in internal factional fighting.
The children were in their father's car, which belongs to the Rafah municipality, when it was struck by a missile in the latest attack on Thursday, witnesses said.
The father was outside the vehicle and escaped unharmed. Two bystanders were seriously wounded.
The Israeli military said the attack was aimed at Palestinian militants firing rockets into Israel. About a dozen such rockets landed in southern Israel on Thursday, injuring at least one high school student.
The strike came as Israeli Prime Minister Ehud Olmert approved additional attacks on Gaza targets, according to a Channel 10 report. Haaretz newspaper reported tank movement at two points several hundred metres within the Gaza Strip.
The Islamic Hamas movement has threatened to respond to the Israeli airstrikes.
"We are ready to send more violent messages" in addition to the rocket attacks, a spokesman for the group said.
An Israeli airstrike two hours earlier killed a bodyguard of Khaled Abu Hilal, a spokesman for the Hamas-run interior ministry, in Gaza City.
At least two Hamas militants were killed in an earlier Israeli airstrike on Thursday as the six-month-old Israeli-Palestinian truce in the Gaza Strip continued to disintegrate.
The two men were killed when their car travelling towards Gaza City was hit. A third man, reported to be a high-ranking Hamas military leader, was seriously injured, a Hamas source said.
Israeli F-16 warplanes also attacked a Hamas security compound in central Gaza City earlier Thursday, retaliating against an escalation in Palestinian rocket fire.
At least one Hamas militant was killed and 32 people were injured, first aid officials confirmed, in the first airstrike on Gaza City since Olmert and Palestinian President Mahmoud Abbas declared the ceasefire on November 25.
At least four Palestinians were also killed on Thursday, as sporadic factional clashes between the rival Palestinian Hamas and Fatah persisted throughout the Strip despite a new internal truce.
Two others died of wounds, raising the total deaths in the worst-ever wave of Hamas-Fatah clashes since Sunday to at least 51.
The three-story building served as the Gaza City headquarters of the Hamas-established Executive Security Force. It was completely destroyed. The dead and four of the injured were members of the force, while the rest were civilian bystanders, many of them women and children, hospital officials said.
An Israeli military spokeswoman confirmed the airstrike, calling the target a Hamas military command and saying it was chosen because Hamas' military wing had claimed responsibility for firing most of more than 70 Gaza-made Qassam rockets launched at Israel since late Monday.
In the ongoing infighting, two Hamas members were killed in the southern Gaza Strip town of Rafah when a funeral for Hamas fighters came under fire. Hamas accused the Fatah-dominated Preventive Security of targeting the funeral.
A 22-year-old woman was also killed. "She was caught in crossfire that followed the killing of the two participants at the funeral," said Mua'wia Hassanin of the Red Crescent ambulance service.
And Hamas accused Fatah of kidnapping one of its militants and executing him "in cold blood" inside the Preventive Security headquarters in Gaza city.
Abbas, of Fatah, cancelled a plan to travel to Gaza on Thursday for a meeting with Prime Minister Ismail Haniya, of Hamas, to discuss boosting the ceasefire.