The military said Palestinian militants fired at least 64 rockets Tuesday at Israeli cities.
Israel has said its troops will not leave Gaza until they have demolished the sophisticated network of Hamas attack tunnels under the Gaza-Israel border and inflicted major damage on the group's arsenal and rocket launchers.
Meanwhile, the miserable living condition of Gaza's 1.7 million people deteriorated even further after two Israeli tank shells struck one of three fuel tanks of Gaza's only power plant. The hit set off a massive fire, and a column of thick putrid smoke rose from the site for hours.
"We need at least one year to repair the power plant, the turbines, the fuel tanks and the control room," said Fathi Sheik Khalil of the Gaza Energy Authority. "Everything was burned."
The shutdown meant that Gaza has an 80 percent deficit of electricity, said Sari Bashi of the Israeli rights group Gisha. Widespread power outages also disrupt water supplies because electricity is needed to operate water pumps. In Gaza, about 1.2 million have no access to running water, she said.
Maher Salem of the utilities department in the Gaza City municipality said about 600,000 of the city's 800,000 residents were facing water problems.
"But the most catastrophic issue for us, which is the ticking bomb, is that once we have run out of fuel (for back-up generators), we have to shut down the waste water treatment," he said, adding that fuel would last up to four more days.
In Washington, State Department spokeswoman Jen Psaki said the Obama administration urges "all parties to respect the civilian nature of these facilities." The Israeli military has not commented on the shelling of the power plant.
Earlier Tuesday, Israeli warplanes carried out dozens of attacks, leveling the home of the top Hamas leader in Gaza, Ismail Haniyeh, and damaging the offices of the movement's Al-Aqsa satellite TV station, a central mosque in Gaza City and government offices.
Haniyeh's house, in a narrow alley of the Shati refugee camp, was reduced to rubble but no one was hurt. Residents placed a large framed portrait of Haniyeh atop the wreckage and draped it with green Hamas flags and Palestinian national banners.
Israel has targeted several homes of Hamas leaders but so far none has been killed. Haniyeh said in a statement Tuesday that "destroying stones will not break our determination."
Meanwhile, two aides to Abbas said the Palestinian leader and the top Hamas official in exile, Khaled Mashaal, are trying to put together a joint delegation that would present Palestinian demands in future cease-fire talks in Cairo.
Abbas and Hamas are former bitter rivals, but took a step toward reconciliation earlier this year when Hamas ceded some power to a technocrat government headed by Abbas.
Egypt has expressed willingness to host indirect talks, but has said the two sides must observe a humanitarian truce of unspecified duration before talks can begin, said the two officials who spoke on condition of anonymity because they were not authorized to discuss internal deliberations with the media.
Alhlou reported from Jerusalem. Associated Press writers Ian Deitch in Jerusalem and Matthew Lee in Washington contributed to this report.