Earlier, Egypt had said that there was "no way" that the bomber or his explosives could have been smuggled through their country.
Investigations into the Eilat bombing, the first to strike Israel's southernmost city, indicated that the 21-year-old bomber (Muhammed Faisal al-Saksak, a resident of the Gaza Strip and member of the Fatah-affiliated Aksa Martyrs Brigades) may not have intended to detonate his explosives pack in a bakery, but planned to execute the attack in a more crowded area.
According to reports by security sources, at least two local residents had spotted Saksak, whose heavy coat and large bag aroused their suspicions, and called the police. Channel 2 reported that one of the people who alerted local police was the taxi driver who took Saksak into town.
Saksak, who appeared to have stopped at the bakery for coffee before reaching his final destination, blew himself up after he saw the police cars approaching.
Three people were killed but only a few wounded in the blast, which occurred at approximately 9:45 a.m.
Director of MDA in Eilat Robert Tolesco said that when paramedics had arrived on the scene, they had found no one in need of medical attention.
Three people arrived at Josephthal Hospital in Eilat following the bombing. All three required treatment for shock, and one woman was also suffering from ringing in her ears as a result of the explosion.
Josephthal Hospital: (08)635-8011
Benny Mazgini, 45, said he was in an apartment across the street when the building shook from the force of the blast.
"It was awful - there was smoke, pieces of flesh all over the place," Mazgini said.
Al Aksa Martyrs Brigades, the Islamic Jihad (which, until recently, refused to sign any cease-fire agreements) and a new terror group calling itself "Army of Believers" claimed joint responsibility for the attack.
Eilat firefighter Shahar Zaid told Channel 2 that the bombing had not resulted in a blaze, and that because the bomber had blown up inside the bakery, the damage had been comparatively contained.
Eilat's police commander said his forces were working to secure the city.
"Our assumption is that it's not one bomber, and there might be more bombers in Eilat right now," Stein said.
Some two hours after the bombing, roadblocks had been erected at all entrances to and exits from Eilat. In addition, police raised the level of alert nationwide.
Only Saturday, Egyptian security forces arrested a 17-year-old Alexandria resident who told a taxi driver in Sinai that he planned to carry out a suicide bombing in Israel.
Egypt said in response to Monday's bombing that there was "no way" that either the bomber or the explosives used could have been smuggled through Sinai, Israel Radio reported.
No suicide attacks have been carried out in Israel since April 17, 2006, when nine people were killed after a bomber blew himself up at a shwarma restaurant in Tel Aviv's old central bus station. Islamic Jihad claimed responsibility for that attack.
AP contributed to this report.