Gaza emergency services said that a woman and a child were killed and 16 people injured in one strike in Gaza City late on Tuesday.
Another eight people were hurt in earlier air raids across the strip, they said.
An Israeli military statement said at least eight rockets were fired at Israel, with six falling on open ground and two more being intercepted by missile defences.
The rocket fire began several hours before a 24-hour truce was to expire, prompting Israel to order its negotiators back from ceasefire talks in Cairo and launch a new round of air strike on Gaza.
They hit at least 10 targets, according to army radio.
The fighting shattered nine days of relative quiet in the skies over Gaza and cast a dark shadow over Egyptian-mediated efforts to hammer out a longer-term truce.
"There has been no progress," Azzam al-Ahmed, the chief Palestinian negotiator in Cairo said on Tuesday. "Matters have become more complicated."
A statement from Hamas spokesman Fawzi Barhum accused Israeli Prime Minister Benjamin Netanyahu of deliberately obstructing truce efforts and said that the militant Islamist movement would now "examine all options in the light of developments in the situation... and facts on the ground."
But Israel's US ally put the blame squarely on the group itself.
"Hamas has security responsibility for Gaza... Rocket fire came from Gaza," State Department spokeswoman Marie Harf said.
"As of right now, with today's developments, we are very concerned and it is our understanding the ceasefire has broken down."
The renewal of Israeli air strikes spread panic among Gaza residents.
An AFP reporter saw hundreds of Palestinians streaming out of Shejaiya, an eastern area of Gaza City which has been devastated by more than a month of fighting between Israel and the militant Islamist Hamas movement.
More poured out of the Zeitun and Shaaf areas, alarmed by a series of explosions and heading to shelter in UN schools, local witnesses said.
An Israeli official said the country's negotiating team had been ordered back from Cairo where Egypt has been pushing for a decisive end to the Gaza bloodshed, which has killed more than 2000 Palestinians and 67 on the Israeli side.
"The Cairo process was based on the premise of a total ceasefire," another official told AFP.
"If Hamas fires rockets, the Cairo process has no basis."
In Gaza, Hamas spokesman Sami Abu Zuhri denied the Islamist movement had fired rockets over the border, accusing Israel of trying to wreck the truce talks.
"We don't have any information about firing rockets from Gaza. The Israeli raids are intended to sabotage the negotiations in Cairo," he told AFP.
But the military wing of the Islamist Hamas said it pounded Israel with rocket fire, hitting Tel Aviv and the southern city of Beersheva.
The Cairo talks centre on an Egyptian proposal that meets some of the Palestinian demands, such as easing Israel's eight-year blockade on Gaza, but puts off debate on other thorny issues until later.
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