Thick black smoke rose from the building. Paramedics said several people were wounded.
Islamic Jihad, a smaller sister group to Hamas, said it believed Harb was the target of the strike.
Israel has killed dozens of wanted militants in surgical strikes throughout the operation, the result, officials say, of intelligence gathered from its collection of high-flying drones overhead and a network of informants.
Before dawn Monday, a missile struck a three-story home in the Gaza City's Zeitoun area, flattening the building and badly damaging several nearby homes. Shell-shocked residents searching for belongings climbed over debris of twisted metal and cement blocks in the street.
The strike killed three adults and a 2-year-old boy, and wounded 42 people, al-Kidra said.
Residents said Israel first sent a warning strike around 2 a.m., prompting many to flee their homes. A few minutes later, heavy bombardment followed.
Ahed Kitati, 38, had rushed out after the warning missile to try to hustle people to safety. But he was fatally struck by a falling cinderblock, leaving behind a pregnant wife, five young daughters and a son, the residents said.
Sitting in mourning with her mother and siblings hours after her father's death, 11-year-old Aya Kitati clutched a black jacket, saying she was freezing, though the weather was mild. "We were sleeping, and then we heard the sound of the bombs," she said, then broke down sobbing.
Ahed's brother, Jawad Kitati, said he plucked the lifeless body of a 2-year-old relative from the street and carried him to an ambulance. Blood stains smeared his jacket sleeve.
Another clan member, Haitham Abu Zour, 24, woke up to the sound of the warning strike and hid in a stairwell. He emerged to find his wife dead and his two infant children buried under the debris, but safe.
In another area of Gaza City, the patriarch of the Daloo family, Jamal, sat in mourning for 11 members of his family killed in a missile strike on his home Sunday. Among the dead were his wife, his son, daughter-in-law, his sister and four grandchildren. He embraced relatives and neighbors paying their condolences, his face swollen from crying. He disputed Israel's initial claim that a senior Islamic Jihad operative was hiding in his house.
The mourners sat in plastic chairs just meters away from bulldozers clearing the ruins of Daloo's home. His 16-year-old daughter Yara was still missing and believed under the rubble, family members said.
Egypt is trying to broker a cease-fire with the help of Turkey and Qatar. Turkish Foreign Minister Ahmet Davutoglu and a delegation of Arab foreign ministers were expected in Gaza on Tuesday.
A senior Egyptian official told The Associated Press that Hamas and Israel were each presenting Egypt with their conditions for a cease-fire.
"I hope that by the end of the day we will receive a final signal of what can be achieved," said the official, who is familiar with the indirect negotiations. He said Israel and Hamas are both looking for guarantees to ensure a long-term stop to hostilities. The official says Egypt's aim is to stop the fighting and "find a direct way to lift the siege of Gaza."
The official spoke on condition of anonymity because of the sensitivity of the indirect negotiations.