Four-year-old twin boys Suhaib and Muhammad were killed instantly when their home in Beit Lahiya was hit by an airstrike. Their parents Foad Hijazi and Amna Hijazi died in hospital. Eighteen people were reported injured in the attack.
Neighbors contacted by Reuters said Hejazi did not belong to any militant group, nor did any organisation claim him as one of their members.
Two firefighters and a paramedic were also injured when a wall of the home fell on them.
Another Israeli airstrike late Monday hit a home in Rafah in south Gaza, killing two teenage brothers and wounded 14 others, two seriously.
Medics identified the brothers as Ahmad Tawfiq al-Nasasra, 17, and Muhammad al-Nasasra, 15.
Thirty-three Palestinians were killed in Gaza on Monday and Israeli shelling intensified across the enclave in the evening.
The bombing of the Hijazi family home comes a day after an airstrike flattened a home in Gaza City, killing 11 members of the al-Dalou family and two neighbors.
Thousands turned out on Gaza's streets to mourn four children and five women of the al-Dalou family.
The bodies were wrapped in Palestinian and Hamas flags. Echoes of explosions mixed with cries of grief and defiant chants of "God is greatest."
Earlier Monday, Israeli forces bombed a tower block that houses several international media offices in Gaza City for the second day. A spokesman of Islamic Jihad's military wing and a 53-year-old civilian were killed.
Israeli attacks on Gaza have killed 115 people and injured over 900 since "Operation Pillar of Cloud" began on Wednesday.