Militants fired rockets at Israel as the conflict entered a second month, both sides defying international efforts to negotiate an agreement for an extended ceasefire.
Medical officials in Gaza said two Palestinians were killed when their motorcycle was bombed and the bodies of three others were found beneath the rubble of one of three bombed mosques.
The air strikes, which lasted through the night, also hit three houses, and fighter planes strafed open areas, medical officials said.
The Israeli military said that since midnight on Friday it had attacked more than 30 sites in the coastal enclave where Hamas Islamists are dominant, without specifying the targets.
Gaza militants fired six rockets at towns in Israel's south yesterday setting off alarm sirens but causing no damage or injuries, a military spokeswoman said.
Violence also picked up in the occupied West Bank, the Palestinian territory where President Mahmoud Abbas's Fatah movement holds sway. A Palestinian man, 43, died of a gunshot wound to the chest in a confrontation with Israeli soldiers in the city of Hebron.
Egypt, helped by American and European mediators, has made no visible progress toward resuming a 72-hour ceasefire that halted the fighting between Israel and Gaza militants, which began on July 8. Egypt was expected to pursue its efforts again over the weekend.
A delegation of Palestinian negotiators stayed in Cairo in the hope of salvaging the ceasefire talks, but participants said the negotiations were not going well. The Palestinian delegation met again late on Friday with Egyptian mediators.
Azzam al-Ahmad, head of the Palestinian delegation, said the delegation would stay in Egypt until it reaches an agreement that ensures the rights of the Palestinian people. "We told Egyptians we are staying," he told reporters.
The Israeli delegation to the Cairo talks left Egypt on Friday morning, and it was not clear if it would return. "There will not be negotiations under fire," Israeli government spokesman Mark Regev said.
The ceasefire expired on Friday with the sides still far apart on the terms for renewing the deal and each side blaming the other for refusing to extend it.
By resuming attacks against Israel, Gaza militants appeared to be trying to ramp up pressure and make it clear they were ready to fight on to achieve the end of a blockade of the territory both Israel and neighbouring Egypt have imposed.
Heavy civilian casualties and destruction in packed residential areas of the Gaza Strip during Israel's campaign against militants have raised international alarm over the past month.
The White House urged Israel and the Palestinians to do what they could to avoid harm to civilians after failing to extend their ceasefire. Spokesman John Earnest said the US is very concerned about the renewed violence.
"We condemn the renewed rocket fire and we are concerned about the safety and security of civilians on both sides of the conflict," Earnest added.
UN Secretary-General Ban Ki-moon issued a similar statement urging the parties "not to resort to further military action that can only exacerbate the already appalling humanitarian situation in Gaza".