The strike came hours after the organisation claimed responsibility for a cross-border raid into Israel, Palestinian security officials have said.
At least four Palestinian fighters entered Israel's Kissufim area on Saturday in a disguised vehicle and exchanged fire with Israeli soldiers, leaving one Palestinian dead.
Islamic Jihad said the raid was carried out by two of its al-Quds fighters and two more from Al-Aqsa Martyrs' Brigades, an armed group loosely linked to Fatah.
"Hamas is trying to draw us [Israel] into their civil war"
Zafon, Beersheva, Israel
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In a statement, the Palestinian journalists' union criticised militants for placing a "TV" insignia on the vehicle they used on Saturday to approach Gaza's border with Israel.
Fighters use of media markings, the union said, could turn journalists who use armoured vehicles in the Gaza Strip into targets for Israeli attack
Hours later, Israel targeted the Islamic Jihad offices.
The Israeli military said a separate air strike hit a weapons production facility. Residents said a dairy truck was hit, but no one was hurt.
The raid on the Israeli checkpoint was the first such infiltration since June 2006 when an Israeli soldier was captured.
The heaviest fighting between Hamas, of which Ismail Haniya, the Palestinian prime minister is a member, and Fatah, the Palestinian president's faction, took place in the southern Gaza town of Rafah, where hundreds of rival fighters took up positions on street corners and rooftops.
|Palestinian fighters used a disguised vehicle|
to raid Israel's Kissufim crossing
Hamas and Fatah pounded each other's positions with rocket-propelled grenades and machine guns, according to locals, who took shelter indoors as the rivals fought block by block.
Hospital sources said two men from Fatah and one from Hamas were killed.
Witnesses said Hamas blew up a house, accusing Fatah fighters of holing up inside it, and that it was hard for ambulances to reach the wounded.
Hamas said the Fatah members had shot dead a Hamas commander in Rafah.
Of the more than 39 Palestinians wounded in the fighting, at least nine were in a critical condition, hospital officials said.
Tensions have remained high in Gaza since an Egyptian-brokered ceasefire between the two factions took effect in mid-May and Sunday's fighting was the worst since the ceasefire was declared.
Burhan Hammad, head of the Egyptian security delegation in Gaza Strip, said that a new ceasefire agreement was reached early on Sunday between Hamas and Fatah in Rafah.
He said the two parties agreed to remove all checkpoints, pull their fighters off the streets and return to a state of calm.
Fatah entered a unity government in March with Hamas in an effort to end factional fighting and to ease international sanctions imposed after Hamas took power.
The embargo has begun to ease, but tensions between the factions has not.
An estimated 616 Palestinians have been killed in factional fighting since the January 2006 election, a leading Palestinian rights group said in a report last Wednesday.