The military confirmed the strike saying it had targeted a "global jihad terrorist" who was linked to a rocket attack on Israel's Red Sea resort of Eilat on April 17.
"A man in his 20s was martyred and another injured in an Israeli air strike... in Shati refugee camp in western Gaza City," health ministry spokesman Ashraf al-Qudra told AFP.
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It was the first deadly Israeli air strike since an Egyptian-brokered truce went into force on November 21.
Witnesses named the victim as a 23-year-old member of a Salafi Islamist group, Haitham al-Mishal.
The military confirmed Mishal was the target, saying he belonged to the Salafi group that claimed responsibility for firing two rockets at Eilat from the Egyptian Sinai.
"A global jihad-affiliated terrorist has been targeted by an IAF (Israeli Air Force) aircraft in the northern Gaza Strip in response to rocket fire towards Israel," the military said.
"On April 17, Mishal was involved in the (Mujahedeen) Shura Council organisation's firing rockets at Eilat," it added, without giving further details.
The Gaza-based MSC claimed the April attack saying it was as a "response to the continued suffering of the downtrodden prisoners in Israeli jails".
Several days later, Israeli Prime Minister Benjamin Netanyahu blamed Gaza militants for the attack and vowed Israel would "exact a price" from them.
"Those who fired them are apparently a terror squad that departed Gaza and used the territory of Sinai to attack an Israeli city.
"We will not accept this and we will exact a price -- this has been our consistent policy the past four years and it will serve us in this case as well," he said in remarks relayed by his bureau.
He reiterated his warnings on Sunday morning, saying Israel would respond in "a very offensive way against any rockets or missiles" fired at the Jewish state.
There has also been an uptick in rocket fire from Gaza on southern Israel over the last two months, despite three months of complete quiet following Egyptian-brokered truce deal which ended eight days of bloodshed in November.
Army statistics show that since the start of this year, 16 rockets fired from Gaza have struck southern Israel, 90 percent of which were fired in March.
Several of those attacks have been claimed by the Mujahedeen Shura Council.
