Israel promised a punishing response to a deadly Palestinian rocket attack Wednesday near the home of the country's defense minister.

The rocket — one of at least eight that struck Israel during the day — killed a 57-year-old woman walking to the grocery store in the Israeli town of Sderot near the Gaza border and raised the specter of a large-scale offensive against militant rocket squads.

Militants affiliated with the Palestinians' ruling Hamas group and Islamic Jihad both claimed responsibility for the fatal Sderot attack, calling it retaliation for 19 civilians killed by Israeli shelling last week in the Gaza town of Beit Hanoun.

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"The occupation hasn't stopped attacking Palestinians before or after Beit Hanoun, so we say resistance is a right of Palestinians," Hamas spokesman Fawzi Barhoum said.

The deadly homemade rocket exploded 150 yards from the home of Israeli Defense Minister Amir Peretz in Sderot. The town of 20,000 is a favorite target of the militants because it is less than a mile from the Gaza fence, but Wednesday's attack was the first deadly strike there since the Gaza Strip evacuation last year.

The rocket also badly wounded a member of the minister's security detail. Another rocket fired later at Sderot seriously wounded a teenager, the rescue service said.

The Israeli defense minister promised a harsh response and convened an emergency meeting of senior security officials. Peretz said Israel will act against anyone involved in firing rockets. "The terror organizations will pay a heavy price," he said.

Prime Minister Ehud Olmert, who is at a meeting of Jewish leaders in Los Angeles, talked to Peretz and generals before the meeting, said his spokeswoman Miri Eisin.

"The operations in Gaza will continue without letup," Olmert told reporters.

Another senior member of the Cabinet, Public Security Minister Avi Dichter, said Israel must expand its operations to bring halt rocket fire, "whether that means a ground operation, an air operation or other special operations."

The area military commander, Maj. Gen. Yoav Gallant, said the army "will get those responsible for the attacks in the way we know how."

Before midnight, Israeli aircraft targeted houses of two leading militants in northern Gaza, residents and the military said. The militants were warned in advance and there were no casualties.

Israel's latest military operation against rocket squads, an offensive in Beit Hanoun, ended last week without major achievements. For more than a week, troops backed by attack helicopters and tanks went after rocket squads in the town. They killed about 50 militants and at least seven civilians, but also left behind badly damaged buildings, uprooted trees and streets chewed up by tank treads. One Israeli soldier died in the offensive.

The Geneva-based U.N. Human Rights Council, which has censured only one country — Israel — during its six-month existence, voted Wednesday to send a fact-finding mission to Beit Hanoun and to condemn the Israeli artillery barrage and other "human rights violations" in the Palestinian territories.

Israeli Ambassador Itzhak Levanon said the special session was another example of the council's lack of objectivity. The United States is an observer of the council, without voting rights.

Rocket attacks resumed from Beit Hanoun immediately after Israeli troops pulled out. On Wednesday, militants fired 13 rockets, eight of which landed in Israel, the military said. Four hit the coastal city of Ashkelon, the northernmost point that Palestinian rockets have reached, although nobody was hurt there.

Although the homemade projectiles are primitive and rarely cause casualties, they have killed eight other people since 2001. Last March a father and son were killed by a rocket blast at Nahal Oz, a village just outside Gaza.

Despite the deaths in Beit Hanoun, which Israel said were unintended, Palestinian talks aimed at forming a more moderate government and ending crippling Western aid sanctions continued.

A coalition agreement would be closely linked to a Hamas-Israel prisoner swap and a promise by Gaza militants to halt rocket attacks on Israel.

Palestinian President Mahmoud Abbas of Fatah met with Egyptian President Hosni Mubarak in Cairo on Wednesday to discuss the talks and the potential for peacemaking. Mubarak told Abbas that Palestinians should "speak in one voice" and express "positions that advance the peace process and end Palestinian suffering."

Envoys of the "Quartet" of Mideast mediators — the U.S., the U.N., the European Union and Russia — also met Wednesday in Cairo to discuss peace prospects. It was their first gathering since Hamas took power in March.

The Islamic militant group insists it will not recognize Israel even after a new government takes power. The moderate Abbas hopes to skirt that problem by a division of labor that would put him in charge of peace talks with Israel, while a government of experts would run daily life in the West Bank and Gaza.

Abbas hopes Israel and the West will accept the premise that Hamas is largely ceding power by making room for a 24-member Cabinet of independent professionals.

Complete coverage is available in FOXNews.com's Mideast Center.