Police killed a second attacker after a doctor found a suicide vest while treating him for wounds suffered in the blast.
The attack fueled Israel's fears that Gaza militants would exploit a border breach with Egypt to sneak into Israel. Militants claimed the bombers entered Israel through the porous Egyptian border, about 35 miles from Dimona, and said more militants were inside Israel waiting to strike.
In Gaza, gunmen fired in the air and relatives of the bombers passed out sweets to celebrate the bombing.
An offshoot of Palestinian President Mahmoud Abbas' Fatah movement claimed responsibility, threatening to complicate recently revived peace talks.
Abbas condemned the violence from his West Bank stronghold. Israeli officials said peace talks with Abbas would continue, but vowed to push forward with the country's military campaign in Gaza, which is controlled by the Islamic militant Hamas. Hours after the bombing, an Israeli aircraft attacked a car in Gaza, killing a senior militant who was involved in rocket attacks on Israel.
Speaking to parliament, Prime Minister Ehud Olmert said Israel is facing a "constant war" against Gaza militants. "This war will continue. Terrorism will be hit. We will not relent," he said.
While Palestinian militants have carried out dozens of suicide bombings since 2000, Monday's attack was the first in Dimona, a working class town of 37,000 in the Negev desert that houses Israel's nuclear reactor. The explosion took place in a shopping center about six miles from the facility.
Israeli officials dismissed suggestions the reactor might have been the target. The facility, where atomic weapons are believed to have been developed, is heavily guarded, enclosed by a 10-foot tall barbed-wire fence and located a mile and a half down a road that is closed to the public. Israel neither admits nor denies it has nuclear arms.
The force of the blast left a surreal scene of strewn flesh and scattered clothing and furry slippers from a bombed-out store. A large bloodstain smeared a wall, rising 20 feet above the ground.
"There was a great explosion and a great ball of fire came toward me," said David Dahan, 58, who was wounded in the blast.
Dahan, who uses walker because of a hip injury, had just finished his morning coffee at a cafe when the bomb went off about 6 feet away.
"I saw him (the bomber) fall. I was hit, but I held on to my walker ... My clothes were covered with his flesh," said Dahan, speaking at a hospital in the nearby city of Beersheba. A bloody bandage covered his eye, and ball bearings were lodged inside his chest and the swollen left side of his face. A leg and arm were also injured.
A second attacker was discovered by Dr. Baruch Mandelzweig, who rushed to treat the wounded. He said he spotted a critically wounded man whose head was moving, and opened his shirt to treat him.
"We saw an explosive belt," Mandelzweig said. "We ran away."
Then police officer Kobi Mor rushed to the scene, where he said he found the bomber on the sidewalk with his explosive belt visible.
"The minute I saw him move his hand toward the belt, I fired and his hand fell," Mor told Channel 10 TV. "Two and a half minutes later he lifted his hand again, again toward the belt, and I knelt down and fired four bullets to the center of his head."
Israeli TV stations repeatedly broadcast footage of the shooting, calling Mor the "hero of the day" and showing the would-be bomber as he lay on the sidewalk, slowly moving his hand toward his midsection. Police awarded Mor a certificate for bravery and gave him a promotion.
Israeli media said 11 people were wounded in the blast.
The United States condemned the attack. "We also condemn those terrorist groups, including Hamas, which condone these horrific actions," the White House said in a statement. "We call upon the leaders of the Palestinian Authority, who condemned this attack, to redouble their efforts to act against terrorism."
Israeli authorities had been on high alert since Hamas militants blew up large sections of the Gaza-Egypt border wall Jan. 23. The breach, aimed at easing an Israeli and Egyptian blockade of Gaza, allowed hundreds of thousands of Palestinians to cross into Egypt.
Egypt managed to reseal the border Sunday. Egyptian officials had no immediate comment on the Dimona bombing.
Egyptian forces and Hamas police exchanged fire at the border Monday, and defiant Hamas leaders warned they would not permit Gaza's only gate to the world to remain closed for long. One Palestinian was killed and at least 44 people - 38 Egyptians troops and six Gazans - were wounded in the worst outbreak of violence since Hamas militants first toppled the border wall.
Israel's 150-mile border with Egypt is mostly unfenced, with few obstacles breaking the long stretch of Sinai desert. In contrast, a complex of fences separates Gaza from Israel.
Abu Fouad, a spokesman for the Al Aqsa Martyrs' Brigades, a violent Fatah offshoot, said the attackers sneaked into Egypt after the border breach, then crossed into Israel using "private contacts." He also claimed the group had more militants inside Israel waiting to strike. The group said it was not under Abbas' control.
Yellow Fatah flags flew outside the home of one of the attackers, 22-year-old Luay Laghwani, and Al Aqsa gunmen fired in the air in tribute to him. His sobbing mother, Ibtissam, held a picture of her son as a young teenager, while male relatives scolded her for crying, saying she should be proud.
She said her son went to Egypt three times after the border was breached, and she last saw him on Wednesday afternoon. He gave no indication he was about to embark on a suicide mission, she said.
The bombing came at a critical juncture. Israeli and Palestinian negotiators relaunched peace talks after a seven-year break just two months ago, and Israel has made it clear it won't implement any accord until Abbas, the moderate Palestinian president, disarms militant groups in the West Bank and Hamas-ruled Gaza.
Hamas violently took over Gaza last June, and Abbas wields no control in the impoverished coastal strip.
Israeli government spokesman Mark Regev said the bombing would not interfere with peace efforts. "Talks will continue, and we will raise this issue of fighting terrorism with the Palestinians," he said.
Abbas' office denounced the attack - but linked the bombing to an Israeli raid in the West Bank that killed two Islamic Jihad militants early Monday.
Hamas spokesman Ayman Taha praised the bombing as a "glorious act."
The last suicide bombing in Israel occurred on Jan. 29, 2007, when a Palestinian attacker entered Israel from Egypt, killing three Israelis in the southern city of Eilat.
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Associated Press writer Diaa Hadid contributed to this report
from Gaza City.
