Palestinians launched more than 130 rockets, mainly at southern Israel, with some intercepted by the Iron Dome anti-missile system, the military said. No casualties were reported on the Israeli side.
Egypt, which has been trying to broker a long-term ceasefire in indirect Israeli-Palestinian talks, said it would continue contacts with both sides, whose delegates left Cairo after hostilities resumed on Tuesday.
But there appeared to be no end in sight to violence that shattered a 10-day period of calm, the longest break from fighting since Israel launched its Gaza offensive on July 8 with the declared aim of ending rocket fire into its territory.
Israeli aircraft have carried out 80 strikes in the Gaza Strip since Tuesday, "targeting terror sites", the military said.
Hamas and medical officials said 19 people died in the latest Israeli raids, including Deif's wife and seven-month-old son. Deif is widely believed to be masterminding the Islamist group's military campaign from underground bunkers.
A Hamas official said Deif, head of Hamas's Izz el-Deen al-Qassam Brigades had not used the targeted house, from which the bodies of three members of the family that lived there were also pulled out of the rubble.
Chanting "Qassam, bomb Tel Aviv!", thousands of Palestinians attended the funeral of Deif's wife and son in Jabalya refugee camp. The woman's mother told reporters she wished she had "another 100 daughters" to offer Deif in marriage.
Accusing Israel of opening a "gateway to hell", Hamas fired rockets at Tel Aviv and Jerusalem late on Tuesday, demonstrating the Islamist movement could still reach Israel's heartland despite heavy Israeli bombardments in the five-week-old conflict.
There was no confirmation from Israel that it had tried to kill Deif, who has been targeted in air strikes at least four times since the mid-1990s. Israel holds him responsible for the deaths of dozens of its citizens in suicide bombings.
"I am convinced that if there was intelligence that Mohammed Deif was not inside the home, then we would not have bombed it," Yaakov Perry, Israel's science minister and former security chief, told Army Radio.
Israeli police minister Yitzhak Aharonovitch, a member of Prime Minister Benjamin Netanyahu's security cabinet, due to convene later on Wednesday, told reporters: "We will continue to hit the heads of Hamas."
Five children were killed in separate air strikes, according to Gaza health officials, and the Israeli military said it had targeted four gunmen in northern Gaza.
Hamas said it fired two rockets at an Israeli gas installation 19 miles off the coast of Gaza in the first apparent attack of its kind. The Israeli military said no missiles had struck any gas platforms at sea.
The Palestinian Health Ministry says 2,036 people, most of them civilians, have been killed in Gaza. Israel says it has killed hundreds of Palestinian militants in fighting that the United Nations says has displaced about 425,000 people.
Sixty-four Israeli soldiers and three civilians in Israel have been killed in the most deadly and destructive war Hamas and Israel have fought since Israel withdrew unilaterally from Gaza in 2005, before Hamas seized the territory in 2007.
Palestinian President Mahmoud Abbas, whose Fatah party took part in the Cairo talks, was due to meet the emir of Qatar, Sheik Tamim bin Hamad al-Thani, and exiled Hamas leader Khaled Meshaal in Doha on Wednesday, diplomatic sources said.
Israel instructed its civilians to open bomb shelters as far as 80 km (50 miles) from Gaza, or beyond the Tel Aviv area, and the military called up 2,000 reservists.
UN Secretary General Ban Ki-moon said in a statement he was "gravely disappointed by the return to hostilities" and urged the sides not to allow matters to escalate.
Egyptian mediators have been struggling to end the Gaza conflict and seal a deal that would open the way for reconstruction aid to flow into the territory of 1.8 million people, where thousands of homes have been destroyed.
The Palestinians want Egypt and Israel to lift their blockades of the economically crippled Gaza Strip that predated the Israeli offensive.