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.
U.N. Security General Ban Ki-moon also arrived in Cairo to appeal for an end to violence.
The rising toll was likely to intensify pressure on Israel to end the fighting. Hundreds of civilian casualties in an Israeli offensive in Gaza four years ago led to fierce international condemnation of Israel.
But Mashaal said Gazans were prepared to keep fighting.
"Gaza's demand is not a halt to war. Its demand is for its legitimate rights," including a stop to Israeli attacks, assassinations and a lifting of the blockade, Mashaal said.
Israel has been jittery that a second front along its northern border could be opened, either by militants in Lebanon or from spillover from the Syrian civil war.
Lebanese military experts dismantled two Katyusha rockets Monday that were equipped with timers and ready to fire at Israel, a senior Lebanese security official said, speaking on condition of anonymity in line with military regulations.
Associated Press writers Hamza Hendawi and Maggie Michael in Cairo and Zeina Karam in Beirut contributed to this report.