The Haaretz daily said the Samouni family, from a suburb of Gaza City, filed the suit at the Nazareth District Court against Olmert, Defense Minister Ehud Barak and the Israel Defense Forces Chief of Staff Gabi Ashkenazi.
Seven family members died when their home was hit by an Israeli tank shell on January 4. Another 22 were killed the next day when Israeli troops attacked a shelter in which family members had taken refuge.
Another 45 family members were injured in the shellings, mainly children, according to a statement by the prosecution, quoted by Haaretz.
The family accuses the Israeli military of "criminal negligence" in killing innocent civilians.
"The plaintiffs' negligence, lack of caution, and violation of duty have manifested in an act of unjustifiable killing," the prosecution statement said.
"The soldiers who fired the shells did so in utter disregard of the innocent civilians present in the area of the fighting."
A three-week Israeli offensive in the Gaza Strip killed around 1,300 Palestinians and injured another 5,000 in December and January. Around 50,000 people were left homeless by the ground and air assault, which was launched in response to the firing of rockets at southern Israeli border towns by Palestinian militants.
