By Dan Williams
JERUSALEM (Reuters) - Palestinian rockets struck two cities deep in Israel on Wednesday, wounding a resident and prompting Prime Minister Benjamin Netanyahu to threaten lengthy "exchanges of blows" with the Hamas-ruled Gaza Strip.
Islamic Jihad, a smaller Gaza faction and occasional Hamas ally, claimed responsibility for the attacks on Beersheba and Ashdod.
They followed Israeli air strikes and shelling in the Gaza Strip on Tuesday that killed four Palestinian civilians, including three children playing football, and five militants, medical officials said.
Netanyahu, who voiced regret for Tuesday's civilian deaths and said Israel sought no escalation, took a tougher tone after some members of his cabinet mooted a wider offensive on Gaza.
Israel's three-week war in the impoverished coastal enclave in 2009 killed about 1,400 Palestinians, drawing heavy international censure. Hamas had mostly held fire since.
"No country would be prepared to absorb protracted missile fire on its cities and civilians, and of course the State of Israel is not prepared to," Netanyahu said in parliament.
"It could be that this matter will entail exchanges of blows, and it may take a certain period of time, but we are very determined to strike at the terrorist elements and deny them the means of attacking our citizens," he said, according to a transcript issued by his office.
By not explicitly mentioning Hamas, Netanyahu may have been trying to distinguish between the dominant Palestinian Islamist movement and other Gazan militants involved in the fighting.
Hamas fired more than two dozen mortar shells and rockets over the weekend, saying it was retaliating for deadly Israeli strikes. But while Hamas cadres went on high alert on Wednesday, they did not appear to be initiating attacks of their own.
Islamic Jihad said it launched three Grads, assembly-line rockets more sophisticated than some shorter-range projectiles Palestinians have used in the past, at Beersheba and Ashdod, 35 km (20 miles) and 40 km from Gaza respectively.
In a statement, Islamic Jihad said it sought to avenge "the Zionist massacres against our fighters and people" and would continue to fight "until the full liberation of our lands" -- a reference to Israel, as well as the West Bank and Gaza.
Hamas, which won a Palestinian election in 2006 and seized control of Gaza a year later, likewise spurns peace with the Jewish state. But in the past it has proposed long-term truces.
Gaza has been kept under grinding embargoes by Israel and neighboring Egypt, while in the Israeli-occupied West Bank, Hamas's U.S.-backed rival, Palestinian President Mahmoud Abbas, has overseen improved security and economic prospects.
With unrest rocking the Arab world, Abbas has broached reconciliation with Hamas, whose forces have cracked down on protests in Gaza.
Israeli Vice Premier Silvan Shalom said the Islamists may have opened a new front with Israel "to stop any possibility of dialogue among the Palestinians or to come to the intra-Palestinian negotiation in a far stronger position".
Speaking on Israel Radio before Netanyahu's remarks in parliament, Shalom said the government would have to consider a fresh offensive in Gaza. A similar prediction was made by Matan Vilnai, Israel's homefront defense minister.
"I say this despite the fact that I know such a thing would, of course, bring the region to a far more combustible situation," Shalom said.
An Israeli military spokeswoman said a Beersheba man suffered moderate shrapnel wounds. Authorities ordered schools closed in Beersheba and advised residents to be ready to take shelter at the sound of sirens.
(Additional reporting by Nidal al-Mughrabi in Gaza; Editing by Janet Lawrence)