Palestinian sources reported that seven people were killed in the blast and at least 40 others were injured.
According to the report, an Israel Air Force aircraft fired missiles at the home, causing great damage to the building and to nearby businesses.
It was also reported that most of the injured, some of whom sustained critical wounds, were civilians and that other people may be trapped under the rubble.
The Hamas police, however, reported that the circumstances of the explosion were unclear. The IDF Spokesperson's Office said that it was unaware of an airstrike in that area and estimated that the blast was the result of a "work accident".
Health Ministry official Moawiya Hassanain said six people were killed, among them a woman. He said 40 people were wounded, including nine who were in critical condition, and that more casualties were being evacuated from the scene.
The Islamic Jihad said Fayed was among the dead, and that the group would carry out reprisal attacks against Israel.
Fragments of locally-produced rockets
Witnesses said Fayed's three-story was flattened by the blast, and that six nearby homes were badly damaged.
Witnesses reported seeing fragments of what looked like locally-produced rockets at the scene, suggesting the house may have been used to store arms.
Two Qassam rockets landed in the western Negev on Thursday, causing damage to a building and hothouses. Two additional rockets hit open areas. There were no reports of injuries.
Several hours earlier, five rockets were launched towards the western Negev, one of them landing in an open area in Sderot. A woman suffered from shock and fell down while fleeing. Another rocket landed outside the city and two fell near the Sapir College.
On Monday, the IDF fired a missile at a car carrying Hamas gunmen in the southern Gaza Strip town of Rafah. Two civilians were hurt in the attack, while the Hamas operatives escaped unharmed. The incident took place shortly after a Qassam rocket landed in an open area near Ashkelon.
A day earlier, a Hamas member was killed and three others were injured in an IDF strike in the Strip. A Hamas gunman's house sustained damage and 11 Palestinians were injured in a separate strike. A third airstrike targeted a Qassam manufacturing workshop.
Barak told the Knesset's Foreign Affairs and Defense Committee that the IDF "is preparing for a large-scale operation in Gaza, its possible alternatives and consequences. We will not deter from any course of action needed to give the residents of Sderot and the Gaza vicinity communities their peace."
The Associated Press contributed to this report