The second Israeli air strike targeted a metal workshop in Gaza's Maghazi refugee camp, killing three Palestinians, including the owner, and wounding two other people, medics said.
Israel said the strike killed the local commander of a rocket production crew with the al-Aqsa Martyrs Brigades of Mahmoud Abbas's Fatah faction.
Israel has bombed metal workshops in the past, alleging that they produce rockets fired at Israel. Witnesses said Saturday's attack was the first carried out during working hours rather than late at night when they were unstaffed.
An Israeli fighter jet later staged two successive raids at the same site where crowds had gathered after darkness fell, wounding five Palestinians, including four members of Hamas's executive force and a civilian, medics said.
Two rockets fired from Gaza shortly after the air strikes struck in the Israeli town of Sderot, injuring one Israeli, the army said.
Hamas radio initially broadcast that three members of its military wing were killed in the first strike but later said this was not accurate.
Abu Mujahid, a spokesman for Popular Resistance Committees, said one of the dead belonged to his group.
On Wednesday, Israeli troops killed at least 11 Palestinians in incursions into the Gaza Strip.
Although Hamas gunmen took part in the fighting and were among the dead, the group appears to be scaling back its military activity against Israel as it struggles to consolidate its hold on Gaza.
Rocket fire and attacks on Israel have diminished significantly since, with Islamic Jihad taking the lead from Hamas.
But Israel has said it would continue to go after armed men preparing attacks on Israelis.