Gaza (CNN) -- An Israeli delegation has been ordered home from talks in Cairo aimed at ending the conflict in Gaza, a senior Israeli official said Tuesday, shortly after the Israeli military blamed militants in Gaza for breaking a truce.
Palestinian negotiators placed the blame for the lack of progress in the talks on the Israelis.
"The Israeli delegation is still trying to impose (upon us) what they want, and this would be impossible for us to accept as Palestinians," said Azzam Al Ahmad, head of the Palestinian negotiators.
The Palestinians introduced their latest position to Egyptian and Israeli negotiators on Tuesday, and are awaiting a response, Al Ahmad said.
By late Tuesday, the armed wing of Hamas -- the Qassam Brigades -- said on its website that it had fired 29 rockets into Israel in 20 minutes.
The Israel Defense Forces, in response, launched airstrikes and ordered bomb shelters open within a 40- to 80-kilometer range of Gaza.
At least three people, including one infant, have been killed, and 52 people have been injured since the breakdown of the ceasefire, according to the Health Ministry in Gaza.
As rocket attacks and airstrikes resumed, one interpretation of the Israelis leaving Cairo was that they had given up on negotiations. Another Palestinian leader, Izzat Risheq, looked at it another way, saying the Israelis took the newest proposal home with them to share with their government.
"The chances of an agreement are very slim, and the situation is very difficult," he said.
In the talks, Israel was calling for Gaza to be demilitarized, demanding that Hamas, which controls the territory, and other militant groups lay down their arms.
Risheq said Monday that the group's weapons were "for self-defense" against Israel.
"But when we have our own Palestinian state with its own national army to protect its citizens, there will be no need for any party to carry any kind of weapons," he said.
Palestinians say Israel's blockade is throttling the economy of the small, impoverished strip of land and the lives of its inhabitants.
Among their demands are the rebuilding and reopening of Gaza's airport and the establishment of a seaport.
But Israeli authorities -- who retain control of Gaza's airspace, Mediterranean waters and their shared border -- say releasing their grip on what goes into and out of the territory isn't feasible while Hamas and other groups are still building up their arsenals of weapons.
The rocket fire came only hours after the ceasefire was extended until the end of the day, as Palestinian and Israeli negotiators, struggling to reach a more lasting agreement, reported little progress.
Israeli Prime Minister Benjamin Netanyahu ordered the IDF to respond to the rockets, a senior Israeli official told CNN. An IDF statement shortly afterward said strikes were being carried out against targets in Gaza.
Nine Palestinians, including three children, were wounded in an Israeli airstrike in Rafah, Ashraf el-Qedra, spokesman for the Palestinian Health Ministry in Gaza, told CNN.
Al Aqsa TV reported airstrikes in northern and central Gaza, as well.
The United States condemned the renewed rocket attacks, with a State Department official reiterating the U.S. position that Israel has a right to defend itself against such attacks.
"We hope that the parties can reach an agreement on a sustainable ceasefire, or if necessary, agree to yet another extension of their temporary ceasefire so they can continue in conversations," Marie Harf, deputy spokeswoman, said.
"But as of right now, today's developments, we are very concerned about and it is our understanding that ... the ceasefire has broken down."
Hamas blames Israel
A thick plume of smoke could be seen rising from a building in southern Gaza apparently hit by an Israeli airstrike.
A CNN team on the ground also saw earlier what appeared to be three rockets being fired from Gaza into Israel, leaving smoke trails in the sky.
Shortly before the rockets were launched, Hamas spokesman Fawzi Barhoum said in an e-mailed statement to CNN: "If Netanyahu does not understand our message and people's demands in Gaza through political language, we know a way to make him understand."
A banner on the Hamas-run Al-Aqsa TV blamed Israel for violating the truce.
The conflict, which began in early July, has killed more than 2,000 Palestinians, leaving entire Gaza neighborhoods in rubble.
The violence has killed 67 people on the Israeli side, with militants in Gaza firing roughly 3,500 rockets toward Israel.
CNN's Frederik Pleitgen reported from Gaza, Jethro Mullen reported and wrote from Hong Kong, and Laura Smith-Spark wrote in London. CNN's Reza Sayah, John Vause, Amir Tal and Andrew Carey contributed to this report.