(CBS/AP) A Palestinian rocket fired from Gaza exploded near the home of Israel's defense minister Wednesday, killing a woman and raising the prospect of a new Israeli military offensive against militant rocket squads.

CBS News correspondent Robert Berger reports that rockets are fired almost daily at the town of Sderot, but this was the first time in more than a year that anyone was killed.

Militants affiliated with the Palestinians' ruling Hamas group and Islamic Jihad both claimed responsibility for the first deadly rocket attack from Gaza since Israel withdrew in September 2005.

They said the rocket fire was meant to avenge the deaths of 19 civilians killed last week in an Israeli shelling in the northern Gaza town of Beit Hanoun.

That deadly strike, which Israel said was unintentional, came after Israeli troops wound up a weeklong incursion in Beit Hanoun meant to curb Palestinian rocket-launching operations there. But rocket attacks continued from other spots in Gaza during the incursion, and resumed from Beit Hanoun after the troops pulled out.

The rocket that fell Wednesday in Sderot landed about 150 yards from the home of Defense Minister Amir Peretz.

Leah Malul, a spokeswoman for Barzilai hospital in Ashkelon, said a woman was killed, a man was critically injured and several passersby were slightly wounded by shrapnel.

Police identified the critically injured man as a member of Peretz's security detail, who was on patrol around the defense minister's house when the rocket hit.

David Baker, an official in the office of Prime Minister Ehud Olmert, said Israel's battle against rocket squads clearly had not ended.

Berger summed up the daily tit-for-tat attacks in the Mideast more bluntly in his report, predicting, "now, it's Israel turn to strike back."

"The continued Palestinian rocket attacks on Sderot and surrounding communities inside Israel are clear evidence that Israel cannot let up in its defense of its citizens and must root out these rocket launchers as well as those who perpetrate these attacks," Baker said.

The army said Palestinians fired a total of 12 rockets on Wednesday; six landed in Israel. Four of the rockets struck the coastal city of Ashkelon, which is the farthest point north that Palestinian rockets have reached.

Although the attacks on the city were not the first, and caused no injuries, they could prompt the military to escalate its response to the attack on Sderot.

The homemade projectiles are primitive and rarely cause casualties, but they have killed eight people since 2001, most recently in July 2005. The near-daily rocket fire has badly unnerved residents of places, like Sderot, that are frequent targets.

Peretz planned to convene a special meeting of senior security officials later in the day.

"Terror organizations will pay a heavy price," he said in a statement.

©MMVI, CBS Broadcasting Inc. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report.

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