The five Palestinians died when Israeli shells hit their house in Gaza City's Shijia district on Friday morning, medics and Hamas members said.
The Israeli attack killed the Hamas fighter and four of his relatives, including his mother and two of her grandchildren.
The deaths came only hours after Israeli tanks and troops pulled out of central Gaza.
Their withdrawal from the area ended a three-day raid which has caused the death of 15 Palestinian fighters and civilians.
The Israeli military re-entered Gaza in an unsuccessful attempt to rescue an Israeli soldier captured by Hamas's armed wing in a cross-border raid on June 25.
The Israeli army also wants to halt Palestinian rocket attacks on Israeli towns and villages.
Israeli armoured forces are still carrying out operations inside parts of northern and southern Gaza.
Israel also continued a vast operation in the West Bank town of Nablus on Friday, where troops destroyed almost all the local Palestinian Authority headquarters, sources on both sides said.
Ahmed Anab, a 38-year-old resident whose house is adjacent to the local muqataa (government office compound), was killed outside his home from the force of explosives detonated by the Israeli army, a medical source said.
A Palestinian security official confirmed that for the third straight day, Israeli forces were working at destroying the muqataa.
"Three bulldozers are destroying it night and day and reducing the buildings to dust," he said.
"The police building, local interior ministry and preventive security building have been entirely destroyed," he added.
An Israeli military source said the object of the operation was to flush out wanted fighters, "some of whom are connected to Hezbollah" whose Shia militiamen have been locked in deadly fighting with Israeli troops in Lebanon.
"They are still exchanging fire and we are using stronger means because they've refused to come out," the source said.
"We have information that the Hezbollah are trying to increase their power in Palestinian territories and are operating in the security forces."