Hamas, which dominates Gaza, named the men as Mohammed Abu Shammala, Raed al-Attar and Mohammed Barhoum, the three highest-ranking casualties it has announced since Israel started its offensive six weeks ago.
All three, killed in the bombing of a house in the southern Gaza town of Rafah, had led operations against Israel over the past 20 years, the Islamist movement said. Hospital officials said a four-year-old girl injured in the attack later died of her wounds.
The Israeli military and Shin Bet, the internal security service, confirmed it had targeted two of the men.
Since the collapse on Tuesday of a 10-day ceasefire, the Israeli military has ramped up its efforts to hit the leadership of Hamas’s armed wing, the Izz el-Deen al-Qassam Brigades.
“We will continue to seek out and target Hamas leaders anywhere, and everywhere – wherever they are,” Israeli Defence Minister Moshe Yaalon said. Hamas said in a statement “the assassination policy has failed to weaken (our) resistance”.
Late on Tuesday, the Israeli air force bombed a house in northern Gaza, an attempt, Hamas said, to assassinate Mohammed Deif, its top military commander. Deif’s wife, daughter and seven-month-old son were killed but Deif escaped, Hamas said.
At a news conference on Wednesday, Israeli Prime Minister Benjamin Netanyahu declined to say whether Israel had tried to kill Deif, but said militant leaders were legitimate targets and that “none are immune” from attack.
Tens of thousands of Palestinians marched at the funeral of the three Hamas commanders on Thursday, firing weapons into the air in anger and calling for revenge.
“The assassinations of the three Qassam leaders is a grave crime,” Hamas spokesman Sami Abu Zuhri told Reuters. “But it will not break our people and Israel will pay the price for it.”
Palestinian health officials said 29 Palestinians, including four children, the Hamas commanders and at least two other militants, were killed in Israeli air strikes on Thursday.
The Israeli military said aircraft attacked more than 30 sites across Gaza and that militants fired more than 70 rockets and mortar bombs into Israel. A mortar bomb that landed near a kindergarten in an Israeli kibbutz badly wounding a parent of one of the children, according to the Israeli ambulance service.
Amos Yadlin, former chief of Israel’s military intelligence and head of Tel Aviv University’s INSS think-tank, said Israel, which was engaged in indirect ceasefire talks with Hamas in Cairo until Tuesday, had now changed its game plan.
“The prime minister has adopted a strategy which says, ‘You shoot at us, we’ll hit you seven times harder, you want attrition? We have intelligence and an air force that will crush you with greater force’,” he told Israel Radio.
However, Israel’s ultimate goal could still be a diplomatic deal to end the hostilities, Yadlin said.
“Even the crazy extremists in Hamas understand time is not on their side and this is what we need to do – military activity aimed at an eventual diplomatic outcome,” he said.
Shin Bet said Abu Shammala headed Hamas’s southern command and it described al-Attar as a brigade commander. It said both had been leading fighting against Israel in the south of Gaza, where some of the most intense combat has occurred.
Israel launched its offensive in Gaza on July 8 with the declared aim of curbing Palestinian rocket fire into its territory. Gaza health officials say 2,061 Palestinians, most of them civilians, have been killed.
Israeli attacks have devastated many areas in the densely-populated enclave, home to 1.8 million people, with 425,000 of people displaced, according to the United Nations.
Sixty-four Israeli soldiers have been killed in the conflict, as well as three civilians in Israel.
Egypt has said it will continue contacts with both sides, whose delegates left Cairo after hostilities resumed. Yet there appears to be little chance in the current circumstances of putting an end to fighting or making progress on peace talks.
Netanyahu said fighting could go on for a long while and provisionally approved the call-up of 10,000 army reservists.
“This will be a continuous campaign,” he told reporters.
Hamas has said it will not relent until the Israeli-Egyptian blockade on the Gaza Strip is lifted. Both countries view Hamas as a security threat and are reluctant to make sweeping concessions without guarantees weapons will not enter Gaza.
The commanders targeted on Thursday were the most senior Hamas men killed since November 2012, when the assassination of military chief Ahmed al-Jaabari triggered an eight-day cross-border war. While Israel says it has killed several hundred Hamas militants in the conflict, they have largely been front-line fighters, not the organization’s commanders-Reuters