The al-Aqsa Martyrs Brigades, the military wing of the ruling Fatah party, said it had fired two missiles early on Sunday morning in response to the killings.
Israel says its warplanes carried out airstrikes in response to rockets fired earlier.
Witnesses said the occupation army carried out four raids on Gaza overnight, but there were no casualties.
An Israeli army spokeswoman said the firing came in response to earlier rocket attacks from the coastal strip into Israel.
“These were reprisals after the Palestinians fired Qassam rockets,” she told AFP.
Israel Radio reported that Shaul Mofaz, the defence minister, had said Israel would respond immediately to any attack on its territory or citizens.
“I have ordered the army to take immediate offensive measures in reaction to the rocket and mortar firing … If calm does not reign in Israel, it will not reign in Gaza,” he said.
After the rocket fire, a military spokeswoman said three explosions had been identified near the border with the Gaza Strip and that the Israeli occupation army had responded with artillery fire aimed at the firing zones.
Palestinian fighters said they fired the rockets in response to the killing of a Palestinian man on a fishing boat by an Israeli naval patrol vessel.
Israel‘s navy has largely blockaded Gaza‘s coast during much of a five-year-old Palestinian uprising, forcing Palestinian boats to stay close to the shore.
Palestinian police were having
Most of the restrictions have remained in place despite Israel‘s Gaza pullout in September.
Meanwhile, five Palestinians, including a police officer, were killed and many were wounded, some seriously, on Saturday as members of two clans clashed in a firefight in Gaza, paramedics and witnesses said.
Palestinian security forces were having difficulty restoring calm, and mediators and bystanders were wounded as bullets and grenades flew in a neighbourhood of the town of Bait Hanun in north Gaza.
The motive for the clash that began on Friday was unclear; but paramedics said at least five of about 40 wounded were in critical condition as family members used assault rifles and rocket-propelled grenades in the clash.