An Israeli woman has been killed in a suicide bombing in the southern town of Dimona, in the first such attack by Palestinian militants in over a year.
The attacker detonated an explosives belt at a shopping centre. Police shot dead an accomplice wounded in the blast before he could detonate his own belt.
It is unclear if the militants, from Gaza, reached Israel via Egypt.
Thousands of Gaza residents surged into Egypt last month when militants blew up the border wall.
The border was finally sealed by Egyptian forces on Sunday, but not before huge crowds of besieged Gazans crossed unchecked into Egypt where they stocked up on much-needed supplies.
Israel had warned that Gaza-based militants could take advantage of the chaos to infiltrate its territory across the long and porous desert border between Egypt's Sinai peninsula and the Negev Desert.
Meanwhile several people are reported to have been injured by gunfire following clashes between Egyptian guards and Palestinians at the Gaza-Egypt border.
The source of the gunfire is not clear but witnesses said youths were throwing stones at an Egyptian checkpoint before shooting broke out.
Condemnation and justification
Nine other people were wounded, one critically, in the blast in Dimona, a remote town that is home to Israel's top-secret nuclear reactor, but never before the target of a militant attack.
"It was like a war. People were running like crazy. I saw a piece of a human being right there, next to my leg," said witness Rosa Enberg.
An al-Aqsa Martyrs Brigades spokesman told a news conference in Gaza that it was a joint operation between al-Aqsa, the Popular Front for the Liberation of Palestine (PFLP) and another lesser-known faction.
The group denied bombers Luai Aghwani and Musa Arafat, both from Khan Younis, had reached Israel from Egypt.
However, Mr Arafat's mother said her son had telephoned her from the Egyptian town of el-Arish.
A spokesman for Hamas, which controls Gaza, said the Dimona attack was "a natural reaction to months of killing" of Palestinians by the Israeli army.
Palestinian Authority President Mahmoud Abbas, whose Fatah party the al-Aqsa Martyrs Brigades profess loyalty to, condemned the bombing.
He also criticised an earlier military raid in the northern West Bank earlier in the day in which Israeli commandos killed two Palestinian gunmen.
Israel was hit by series of suicide bombings in the 1990s and 2000s, peaking after the Palestinian intifada or uprising broke out in 2000.
However, there were only two such attacks between April 2006 and now, the last being in January 2007 when a bomber blew himself up in a bakery in Eilat, killing three people.
Monday's blast is also the first since renewed efforts to come to an Israeli-Palestinian peace deal were launched with US support last November.
Hours later, Israeli aircraft assassinated the top military commander of the Popular Resistance Committees, Amer Qarmut, alias Abu Said.
Prime Minister Ehud Olmert told a meeting of his Kadima party that Israel was fighting a "relentless war... against anyone who tries to harm Israeli citizens".
Israel argues that restrictions it imposes on about four million Palestinians in Gaza and large parts of the occupied West Bank are crucial in preventing such attacks, though the blockades have been condemned as "collective punishment" by the UN.