Israeli jets have carried out at least five air strikes against the Gaza Strip in which 17 people were wounded, Palestinian emergency workers said.
The Israeli military had no immediate comment.
The attacks came after Hamas militants in Gaza offered to stop cross-border fire into Israel if the Israelis halted attacks on Gaza.
The group's armed wing, the Ezzedine al-Qassam Brigades, which lobbed about 50 mortar rounds into Israel, made the offer in a statement released after Israeli aircraft raided the enclave again.
It said barrage had been in response to an Israeli strike which killed two of its members, but that it was ready to call an end to the tit-for-tat violence if Israel also did so.
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"If the enemy stops the escalation and aggression against our people we will implement the Palestinian national agreement," the statement said, referring to a truce reaffirmed by the main militant factions in January.
Israeli military and government officials declined to comment on the statement, but the Jewish state's often-stated standing policy is to "respond forcefully" to every Palestinian attack.
In a later statement, Hamas spokesman Taher al-Nunu said the movement's Gaza government was committed to preserving the informal truce, with the backing of other militant groups.
"The government affirms that there is consensus among the factions regarding the security situation in the strip," he said in a statement.
Shortly before the Ezzedine al-Qassam Brigades offer, Israeli warplanes raided the Gaza Strip, slightly wounding one man, local witnesses and medical officials said.
Witnesses said the target of the raid was a car repair workshop east of Gaza City, owned by the powerful Doghmush clan which has links to Islamic militants.
The Israeli military, however, said its aircraft hit what a spokeswoman described as "a terrorist tunnel" intended to launch attacks under the Gaza border fence into Israel.
Israeli Deputy Foreign Minister Danny Ayalon issued a death threat against Hamas leaders.
"If Hamas decides to escalate, we will put an end to it ... We have several actions before putting ground forces in Gaza, including direct threats against Hamas leaders," Ayalon told public radio.
A rocket fired from Gaza exploded in southern Israel, causing neither casualties nor damage, several hours after another rocket exploded harmlessly in the town of Ashkelon.
After the mortar fire Israel pounded Gaza, wounding at least five Palestinians and cutting power supplies.
The mortar attacks, the fiercest since Israel carried out a 22-day offensive codenamed Operation Cast Lead against Gaza rocket fire in December 2008 and January 2009, wounded two Israelis and caused minor damage.
In January 2011, Gaza's main militant factions confirmed a year-old truce after weeks of increased rocket fire and spiralling tensions along the border prompted a warning from Arab leaders that Gaza risked a major new Israeli invasion.
Israeli opposition leader Tzipi Livni called for just that in response to the mortar barrage.
"The right way to deal with it is with force, just like Israel did during and after Operation Cast Lead," news website Ynet quoted her as telling local authority heads in the border region.
