A Palestinian suicide bomber who may have sneaked into Israel from the Egyptian Sinai blew himself up at a shopping center in this southern desert town on Monday, killing an Israeli woman and wounding 11 other Israelis, emergency services officials said.

A second attacker with him failed to detonate his explosives belt and was shot dead by a police officer at the scene.

The bombing broke a year of relative calm in Israel, and was the first in Dimona. The country’s last suicide attack came in late January 2007, when three Israelis were killed in the southern city of Eilat.

In Gaza, Al Aksa Martyrs Brigades, a militia loosely affiliated with the mainstream Fatah movement of President Mahmoud Abbas, claimed responsibility for the attack, saying it had been carried out in conjunction with the Popular Front for the Liberation of Palestine and a previously unknown group calling itself the National Resistance Companies.

The militant groups identified the two attackers as Palestinian residents of the Gaza Strip, which is currently controlled by the militant Islamic group Hamas.

The bomber who blew himself up, Louai al-Aghwani, 21, of Gaza City, was said by his family to have been a Fatah supporter. The second attacker was said to be Musa Arafat, 23, a Popular Front activist from a village near Khan Yunis in the south of the strip. He is not known to be any relation of the late Palestinian leader Yasir Arafat.

The declared involvement of the Brigades attests to the fractured nature of Fatah, whose West Bank-based leaders are in peace talks with Israel. Militants in the group, particularly in Gaza, do not necessarily take instructions from Mr. Abbas, who says he opposes suicide attacks and firing rockets into Israel.

In a statement on Monday, the Abbas-led Palestinian Authority condemned the Dimona attack.

Hamas did not initially claim any part in the bombing, but a spokesman for the movement, Sami Abu Zuhri, called it “heroic.” Late Monday, Reuters reported that the military wing of Hamas had also claimed responsibility. Adding to the confusion, an unidentified source from Hamas told Reuters that the bombers had entered Israel not from Gaza or Egypt, but from Hebron in the West Bank.

Spokesmen for the militia sent out contradictory messages about how the bombers had reached Dimona, a relatively remote working-class town in the Negev desert that is best known for its proximity to Israel’s nuclear reactor. The heavily guarded reactor lies about six miles outside the town.

At first, a Brigades spokesman said the two had taken advantage of the recent breach of the border between the Gaza Strip and Egypt, crossing from Gaza into the Egyptian Sinai and from there into Israel south of Gaza, in the open desert. But in a later statement the Brigades denied that, possibly to avoid further friction between Gaza and Egypt, saying the men had entered directly from Gaza.

The Israeli authorities had warned in recent days that Palestinian militants had taken advantage of the breach of the border, which occurred after Hamas blasted sections of a wall between Gaza and Egypt on Jan. 23. Egyptian forces resealed the border on Sunday.

The suicide attack took place at about 10:30 a.m. at the entrance of a covered alleyway between a lottery ticket kiosk, a candy store and a shop selling jewelry, cosmetics and knickknacks.

Charlie Ifergan, 50, the jewelry store owner, was standing at the cash register when the explosion occurred but was unhurt. He was protected by a shop wall that absorbed the blast, he said. He added, “At first I thought it was an electrical short circuit, but then I saw half a corpse next to me, and I understood it was an attack.”

Many residents of this usually quiet town were shocked that terror had struck here. “It won’t go back to being what it was,” said Shimon Zaguri, 42, a taxi driver. “People used to sit here and drink coffee without a care in the world. Now they’ll be looking all around.”

Esther Peretz, 41, was on the way to the shopping center after celebrating her son’s bar mitzvah when the bomb went off, missing it by minutes. “I feel like I’ve been saved,” she said.

The Israeli victim of the bombing was identified late Monday as Liuvov Razdolaskya, 73, according to the Israeli Web site Ynet.

The bodies of the attackers lay on the ground for hours behind a police cordon, as sappers, or explosives experts, worked to ensure that both their belts had been neutralized, and volunteers gathered pieces of flesh from the road and from car hoods.

The men’s bodies, one with the head blown off, lay amid plastic body parts of mannequins from a nearby clothing store. Local youths snapped photos of the macabre scene on cellphones as the police tried to keep them back.

Kobi Mor, 34, the police officer who shot the second attacker, said he approached the man as he lay on the ground, apparently wounded from the first blast, then shot him when he moved his hand toward an explosives belt strapped to his abdomen.

“I saw he was alive, and his hand was twitching,” Mr. Mor told reporters. “He raised it again to try to activate the bomb, so I shot four bullets into his head and neutralized him.”

After the bombing, the police services went on high alert in various areas of the country, and officers were stationed at main junctions on roads in the south.

In the Sabra neighborhood of Gaza City, the family of Mr. Aghwani described him as a former tailor who had been out of work for a year. One of 10 children, he had left school after the sixth grade, they said.

According to his mother, Mr. Aghwani left the Gaza Strip for the first time in his life on the first day that the border with Egypt was breached, shopping for her in the Egyptian border town of Rafah. He went in and out of Egypt several times over the next few days, leaving the house for the last time on Wednesday, the family said.

Few suicide bombers have succeeded in getting into Israel from Gaza in the past. Gaza’s borders with Israel are well patrolled by the Israeli Army and are surrounded by a security fence.

Tensions flared again late Monday on the border between Gaza and Egypt. Witnesses said dozens of Palestinians stranded on the Egypt side had gathered at the border demanding to be let back into Gaza, and started throwing stones at the Egyptian forces stationed there. Armed clashes erupted and one Palestinian was killed, said medical officials and Hamas. About 16 Palestinians and Egyptians were wounded.

Over the past few days, the Egyptian authorities reported the arrests of more than a dozen Palestinians carrying weapons and explosives in the Sinai Peninsula, close to the border with Gaza. At least two were found with suicide bomb belts, according to news reports.