Two Palestinians were also wounded in the evening raid in the northern Gaza Strip yesterday, the emergency services said.
The dead man, 30-year-old Mohammed al Awour, and one of the wounded were travelling on a motorbike and were the apparent targets. A seven-year-old boy who was passing by on foot was also wounded.
The Israeli military said it had targeted "terrorists affiliated to the international jihad," its designation for Al-Qaeda inspired groups in Gaza.
Al Awour was involved in numerous rocket attacks on southern Israel in recent years and particularly over the past month, the Israeli army said in a statement.
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He belonged to an "a violent and extremist Salafist cell which attempted to organise several terrorist attacks against Israel," the army statement added.
Abbas, who swore in a new merged government for the Palestinian territories last week replacing the Hamas administration in Gaza, condemned the rocket fire which Israeli officials said hit the Eshkol region without causing any casualties or damage.
Now, Prime Minister Benjamin Netanyahu holds Abbas, who heads the unity government, responsible, a spokesman said.
"Abbas is responsible and accountable for rockets that are fired at Israeli towns and cities by terrorists in the Gaza Strip," Ofir Gendelman said on Twitter.
Netanyahu welcomed the deadly Israel air raid and promised that the army and the Shin Bet security service would "continue to take strong action against all those who try to attack the security of Israel's citizens."
Reacting to the rocket fire, Abbas's office said he "condemns the rocket fire and calls for honouring past agreements."
"We condemn all rocket fire from Gaza. It is unprovoked aggression against civilian targets and is totally unacceptable," State Department spokeswoman Jen Psaki said.