An Israeli air strike in Gaza killed the wife and infant son of Hamas's military leader, Mohammed Deif, the group said, calling it an attempt to assassinate him after a ceasefire collapsed.
Palestinians launched more than 180 rockets on Tuesday and Wednesday, 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 the 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 more than 100 strikes in the Gaza Strip since Tuesday, Defence Minister Moshe Ya'alon said, the military adding it was "targeting terror sites".
Hamas and medical officials said 23 people had 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 whose rubble the bodies of three members of the family that lived there were also pulled out.
Abu Ubaida, a spokesman for Hamas's armed wing, said in a televised statement addressing Israel "you have failed and you have missed" Deif in the attack.
Chanting "Qassam, bomb Tel Aviv!", thousands of Palestinians later 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 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.
"ALL OPTIONS OPEN"
Prime Minister Benjamin Netanyahu declined to say whether Deif had been targeted, but he reaffirmed Israel's longstanding policy of considering militant leaders as legitimate targets, adding that "none are immune" from attack.
Netanyahu said Israel's Gaza campaign could last for a while. "This will be a continuous campaign," he told a news conference in Tel Aviv, giving a vague description of Israel's goals as seeking "calm and safety" for Israeli citizens.
Ya'alon, his defence chief, added that "all options are open, including renewed ground operations" in Gaza.
Netanyahu compared Hamas Islamists to Islamic State militants operating in Iraq and Syria, calling them "branches of the same tree" and accusing both groups of acting with "savagery" by killing and targeting attacks against civilians.
Abu Ubaida, the Hamas military spokesman, said the group would target Israeli public sites such as soccer stadiums and Israel's Ben-Gurion International Airport. He warned airlines to stay away from Thursday morning and cautioned Israelis living near to Gaza against returning to their homes.
An Israeli airport spokesman said there were no disruptions reported in Thursday's flight schedules.
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 had fired two rockets at an Israeli gas installation about 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 2,040 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, Sheikh 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 50 miles from Gaza, or beyond the Tel Aviv area, and the military called up 2,000 reservists.
U.N. 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.
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The U.N. Security Council expressed "grave concern" Wednesday at the resumption of hostilities in Gaza between Israel and Palestinians and called upon the parties to resume negotiations to urgently reach a "sustainable and lasting ceasefire."
The 15-member Security Council also "called upon the parties to prevent the situation from escalating and to reach an immediate humanitarian ceasefire," said British U.N. Ambassador Mark Lyall Grant, president of the council for August.