Hamas' claim of responsibility raised the likelihood of even heavier fighting with Israel. Six of the militants were killed in an Israeli airstrike on a police station.
Hamas retaliated with a rocket barrage on the southern Israeli town of Sderot. The rockets hit a house and seriously wounded one person, police and rescue workers said. Electricity was knocked out in part of the town, plunging it into darkness.
Abu Obeida, spokesman for Hamas' military wing in Gaza, told the group's radio station that the attackers came from the West Bank city of Hebron. He said they managed to carry out the bombing despite Israel's security control of the area and "bring a nightmare" to the southern Israeli town of Dimona.
Before the announcement, there had been conflicting theories about the origins of the attack, which killed a 73-year-old Israeli woman, critically wounded her husband and injured 10 other people.
Despite initial suspicions that the bombers were from Gaza, Israeli officials grew skeptical of that claim and turned the focus of their investigation to Hebron. Israeli media said pictures of the alleged attackers released in Gaza did not match the appearances of the two suicide bombers.
"Most likely ... the terrorists did not come from the border with Egypt, but most likely they came from the area of Mount Hebron," Israeli Cabinet Minister Zeev Boim told Israel Radio.
Dimona is about 40 miles from the Egyptian border, and about the same distance from Hebron.
The Hebron connection to the attack could cloud recently revived peace efforts with moderate Palestinian President Mahmoud Abbas who controls the West Bank. Although the Israeli military has a heavy presence in the West Bank, it has also demanded that Abbas do a better job reining in militants there.
In Monday's attack, two attackers entered Dimona with explosives belts strapped to their bodies. One blew himself up, but the second was injured in the blast, and police shot him to death before he could detonate his bomb.
Hebron is a militant center dominated by Hamas, which also rules the Gaza Strip. It is in the southern West Bank in an area not yet set off by the barrier Israel is building to keep out West Bank attackers. In 2004, Hebron suicide bombers killed 16 people in a twin attack in the southern Israeli city of Beersheba.
Earlier Tuesday, Israeli Defense Minister Ehud Barak pledged "to find a solution to the terror from Hebron."
Hamas identified the two attackers as Mohammed Herbawi and Shadi Zghayer, members of two families from Hebron. Palestinian officials said Israeli troops had arrested relatives of the two men.
Relatives said both had served terms in Israeli prisons.
Confusion about the origins of the militants stemmed from Israeli concerns that more than one militant cell had tried to infiltrate Israel.
Israel launched new attacks on Gaza militants Tuesday. Two Hamas militants were killed in clashes with Israeli troops in the southern Gaza Strip. Israeli aircraft later killed six people in an airstrike on a Hamas police station.
Israeli troops have been on high alert since Gaza militants blew up the border with Egypt on Jan. 23, allowing hundreds of thousands of people to pour into Egypt unchecked over 12 days. The Egyptians managed to reseal the border only on Sunday.
In Gaza on Monday, the Al Aqsa Martyrs' Brigades - a violent offshoot of Abbas' Fatah movement - provided the names of the men it said were the bombers and a detailed account of how they sneaked into Israel from Egypt. The families of the two young men were mourning.
On Tuesday, the group continued to insisted that it carried out the attack.
Although the attack in Dimona complicated peace efforts, it didn't derail them. Late Monday, Israel's chief negotiator, Foreign Minister Tzipi Livni, met with the lead Palestinian negotiator, Ahmed Qureia.
Still, Israel has insisted repeatedly that it would not implement any peace deal with the Palestinians until militant groups in the West Bank and Gaza are dismantled. Abbas has not yet done that in the West Bank and is in no position to do so in Gaza, where Hamas militants overpowered his security forces in June and took control.
Israeli police, meanwhile, were out in higher numbers Tuesday at entrances to cities, shopping malls and bus and train stations.
Overnight, border police arrested 240 Palestinians who had entered Israel illegally to work, police spokesman Micky Rosenfeld said.
The claim that the bombers entered Israel from Egypt has revived a long-standing proposal to build a barrier along the 150-mile border with Egypt.
Israel's desert border with Egypt is mostly open, with few obstacles. By contrast, a large fence complex separates Gaza from Israel, and attacks from the seaside territory have been rare.
