The airstrike targeting Palestinian militants came just hours after Palestinian leader Mahmoud Abbas demanded that militants end rocket attacks on Israel or be responsible for reprisals.
Around 14 people were wounded in the strike, including five children.
The Israeli military said the car was carrying militants from the Al Aqsa Martyrs’ Brigades, which is affiliated with President Abbas’s Fatah movement.
Israeli authorities claimed the men were implicated in planning attacks on Israel. Witnesses said the militants jumped out of the car before the blast.
The dead children included a five-year-old boy and a seven-year-old girl, according to Dr Jumma Fatah of Shifa Hospital in Gaza City.
The car exploded on a narrow street in the crowded refugee camp. The front of the car was badly damaged, but the back was intact. Hundreds of angry Palestinians gathered around the vehicle, shouting slogans.
Mr Abbas released a statement saying he “condemned this new crime, at a time when the Palestinian leadership is making efforts to preserve the ceasefire”, and urged the international community to “fulfil its responsibilities to stop the Israeli escalation”.
Hours earlier, Mr Abbas’s office said he had called on all armed groups “to cease firing rockets immediately and to fully respect the truce” agreed by the main militant groups early last year.
“Any faction that does not respect the truce will bear the entire responsibility for the destruction and casualties that will result from an Israeli aggression against the Gaza Strip,” Mr Abbas said.
“Red flash”: witness
Khalil Roka, a cousin of the dead boy, said he was sitting in front of his car repair shop while the children played in front of the house nearby.
He said he saw a red flash, the car exploded and the children were hit, but he did not see the child who was killed. “I was carrying my other cousins to the ambulance,” he said.
Israel’s Channel 2 TV said the raid was “another failed assassination attempt, and again innocent civilians were hit”.
An air strike last week killed eight civilians, in addition to the two militants it targeted.
The latest violence comes after eight family members were killed in an explosion at a beach that Palestinians blamed on Israeli artillery fire. Israel has denied involvement in the blast.
About 100,000 Palestinians live in the Jebaliya camp, just north of Gaza City, making it the largest refugee camp in Gaza. The poverty-stricken camp is a main breeding ground of militants.
Israel has often targeted Palestinian militants by firing missiles at their cars from aircraft.