In one airstrike, Israeli warplanes struck a target in the town of Khan Yunis, but no casualties have been reported from that attack yet.
Medical sources say a five-year-old was among the fatalities of the attacks carried out late on Friday.
The Israeli airstrikes began on Thursday, shortly after eight Israelis were killed near the Red Sea resort town of Eilat.
Dozens of Palestinians have also been injured in the attacks.
Israeli officials have blamed a Gaza-based militant group called the Popular Resistance Committee (PRC) for Thursday’s attack and have vowed a “full force” response targeting Gaza.
Israel said the attackers had infiltrated from the Hamas-run Gaza Strip, although the PRC, which is not affiliated with Hamas, denied involvement in the incident.
Hamas has said that it had nothing to do with the assault and has warned against any act of aggression against the Gaza Strip.