A Palestinian rocket on Wednesday landed in a southern Israeli community, lightly wounding two preschoolers with shrapnel as they played outside their home, Israeli medics said.

Officials said the rocket struck a home in Kibbutz Beeri, a collective farm about 4 miles from the Gaza border. They said the wounded children were siblings aged 2 and 4. Police said the children were in their yard at the time of the attack.

The ruling Hamas militant group in the Gaza Strip claimed responsibility, raising the likelihood of an Israeli reprisal.

"These rockets are being fired indiscriminately into civilian population centers. We are obliged as a government to take the necessary steps to protect our people and we will continue to do so," said Israeli government spokesman Mark Regev. "Those extremists shooting rockets are a legitimate target and we will act surgically to strike against hardcore terrorist cells."

Earlier Wednesday, Hamas militants fired rockets at Israeli border communities, and an Israeli airstrike against rocket squads wounded four militants, the Islamic group said.

Hamas said it had fired 31 rockets into Israel since Tuesday in retaliation for an Israeli airstrike that killed six people.

Israel vowed to maintain the siege of the Gaza Strip until its Hamas rulers halt attacks.

Hamas moderately wounded a 14-year-old girl and knocked out power in parts of the rocket-scarred Israeli town of Sderot with a barrage of rockets fired at border communities Tuesday and early Wednesday.

Gaza militants said Israel responded with several airstrikes overnight, but the military confirmed only one, saying aircraft had fired at militants who had just launched rockets. Hamas said four of its men were moderately wounded.

Israel indicated that it would not let up in its attacks on Hamas.

"We need to understand there is a war in the south," Israeli Vice Premier Haim Ramon told Israel Radio. "The war against Hamas has to be fought on all fronts."

Israel will continue to use the "economic weapon" against the Gaza Strip, and reduce supplies of fuel, electricity and some food to the territory in an attempt to persuade Hamas to stop the rockets, Ramon said.

Israel cut off virtually all shipments into Gaza three weeks ago after Hamas barraged Israel with rockets following an Israeli operation that killed 19 Gazans, most of them militants.

Hamas also took responsibility for a homicide bombing Monday in the southern Israeli town of Dimona. The Islamist group's first homicide attack in Israel in three years underscored its ability to hamper U.S.-backed efforts by moderate Palestinian President Mahmoud Abbas to reach a peace deal with Israel by the end of the year.

• Shop Owner: Bomber Demanded Coffee, Then Blew Up

• Reporter's Notebook: Suicide Attacks in Israel

Israel insists on an end to violence before it implements any peace agreement, but Abbas has had no control over the Gaza Strip since Hamas seized control there from his forces in June. Monday's bombers came from the West Bank, not Gaza, giving greater weight to Israel's demand that Abbas take stronger action against militants in the West Bank, too.

Abbas on Wednesday condemned the rocket fire, but urged Israel to let supplies into Gaza.

"These rockets that are being fired at Israel must stop. It's pointless," he said at a news conference with Austrian Foreign Minister Ursula Plassnik. "At the same time, Israel should not use these rockets as a pretext for collective punishment on Palestinians in Gaza. Israel must always allow humanitarian supplies and other needs to be provided to Gaza."

In the West Bank city of Hebron, relatives of Shadi Zghayer and Mohammed al-Herbawi said they learned from watching Hamas' Al Aqsa TV that the two were identified as the Dimona bombers. The two Hamas members in their 20s left home early Monday, without saying where they were going, relatives said.

A farewell video of the two bearded bombers that Hamas released Wednesday showed them holding guns and standing in front of Hamas flags.

"I, the living martyr Mohammed Karim Mohammed Hijazi al-Herbawi ... sacrifice myself for the sake of God, for the sake of those who are besieged in Gaza, and in response to the crimes of the Zionist occupation," said the militant, who was wearing a green Hamas headband.

Israeli government spokesman Mark Regev said he expected the Dimona bombing to strengthen the resolve of the international community to shun Hamas.

"I hope that this public admission by Hamas of direct involvement in the deliberate targeting of innocent civilians will serve as a wake-up call to those in the international community who've had illusions as to the true nature of Hamas," Regev said Tuesday.