According to the survivors' accounts, partly corroborated by the International Red Cross and the United Nations, shells and missiles fired by the Israeli military hit the house the following day, leaving 29 people dead.
"This was a barbaric action. They said that there was resistance here, and I don't know what. But there was no resistance," Naela al-Samouni, one of the survivors, said.
Two months after the attack, the remaining al-Samounis live in a makeshift tent amid the rubble of their former home.
Tuesday's lawsuit names Olmert and Ehud Barak, the Israeli defence minister, as defendants, and accuses the Israeli military of "criminal negligence" for killing innocent civilians.
Mohammad Fukra, a Palestinian Israeli attorney, filed the lawsuit on behalf of the al-Samouni family, saying the family had the right to sue Israel and its officials.
Israeli courts in the past have, however, rejected claims from Palestinians harmed in conflicts.
Mark Regev, an Israeli government spokesman, has claimed the Palestinian group Hamas was responsible for the deaths, saying the group used civilians as human shields.
Israel undertook the Gaza offensive with the purported aim of stopping rocket fire from the territory into southern Israel.