The latest strikes targeted two camps of the armed wing of Hamas, the Ezzedine al-Qassam Brigades, in central and northern Gaza, and a former Hamas security post in Gaza City. They wounded about 20 people.
An Israeli army statement early Saturday confirming the latest operations said they were in response to rocket fire earlier in the week into southern Israel.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
Israel held Hamas responsible for "all terrorist activity coming from the Gaza Strip," the army statement added.
On Friday, medics in the Gaza Strip reported that two Palestinians had been killed and four wounded when Israeli warplanes struck twice.
A first Israeli air strike on Friday afternoon targeted the east of Al-Bureij in the central part of the Gaza Strip, killing Basel Ahmad, 29, who was of no known affiliation, local medical sources said.
Two other Palestinians were wounded in the strike, one of them seriously, the sources added.
Israeli aircraft "targeted a terrorist squad during preparations to fire a rocket at Israel from the central Gaza Strip. A hit was identified," the military said in a statement.
A second Israel air strike killed another Palestinian in the north of Gaza.
Hammam Abou Qadous, 20, died of his wounds after being hit as he travelled on his motorbike in the northern part of the Gaza Strip Friday evening, Palestinian medical sources said.
Two other Palestinians were slightly injured in the same attack, they added.
An Israeli army statement said "a plane of the Israeli Air Force targeted a terrorist group in northern Gaza just after the group launched a rocket that hit the Ashkelon region".
Earlier on Friday, Palestinian militants in Gaza fired two rockets that hit southern Israel, without causing casualties or damage.
The violence came despite a tenuous Egyptian-brokered truce between Israel and Gaza's Hamas rulers. It was announced late Wednesday by the Islamists' Ezzedine al-Qassam Brigades military wing after a flurry of deadly exchanges in and around the territory.
The latest round of Israeli attacks and Palestinian retaliation began with air strikes Monday morning, just hours after gunmen from Sinai carried out an ambush along Israel's southern border with Egypt, killing an Israeli civilian.
Israel has said that its sudden spike in Gaza operations was "in no way related" to the border incident, with the military saying the air force was targeting militants about to attack the Jewish state.
Since Monday, more than 130 rockets and mortar rounds have been fired at Israel, one of which slammed into a border police post just north of Gaza, wounding four people.
The Hamas military wing said on Thursday that it had fired 120 rockets, a rare show of force from the Islamist group that had previously been observing a de facto truce.
