The rare violence in that part of the country targeted a passenger bus, a military patrol and a private car, the officials said. Channel 10 TV reported a fourth attack, but there was no official confirmation or details. The military said a "large number" of assailants were working in multiple squads.
"We are talking about a terror squad that infiltrated into Israel," said Israeli military spokeswoman Lt. Col. Avital Leibovich. "This is a combined terrorist attack against Israelis."
The violence near the resort city of Eilat stoked concerns about growing lawlessness in neighboring Sinai following the ouster in February of Egypt's longtime autocratic leader, Hosni Mubarak.
Last week, Egypt moved thousands of troops into the Sinai Peninsula as part of a major operation against al-Qaida inspired militants who have been increasingly active in Sinai since Mubarak's ouster in February. The militants have taken advantage of the security vacuum caused by the abrupt withdrawal of police forces. Authorities have blamed the militants for brazen attacks on police patrols as well as a string of bombings on a key pipeline carrying natural gas to Israel and Jordan.
"The incident underscores the weak Egyptian hold on Sinai and the broadening of the activities of terrorists," Israeli Defense Minister Ehud Barak said in a statement. "The real source of the terror is in Gaza and we will act against them with full force and determination."
Bedouins in Sinai cooperate with anti-Israel militants in Gaza, just across the border.
The driver of the bus said he had seen Egyptian soldiers open fire, but military spokesman Brig.-Gen. Yoav Mordechai said he was not aware of any Egyptian military involvement.
Israeli security forces tracked down some of the assailants and are engaged in an ongoing gunbattle with them, Mordechai said. The attackers fired mortars and an anti-tank missile, he said. The military spokesman's office said a roadside bomb was detonated when a military patrol arrived at the scene of the bus attack and drove over the device.
Mordechai said the nature of the attack indicated that it had been well planned.
The military said several assailants had been killed in the shootout with Israeli forces, but did not give a number.
A doctor at the main hospital in the area said the medical facility had been put on an emergency alert. Israel Radio said roadblocks were thrown up in the area and that entrances and exits to Eilat were sealed. Senior Israeli defense officials convened in emergency session at the defense ministry in Tel Aviv.
Israel Radio reported an explosion in another southern town about 150 miles (230 kilometers) away, Beer Sheba, but the gunfire there was unrelated, Channel 10 TV said.
In Egypt, a senior security official denied that the attackers crossed into Israel from the Sinai Peninsula or that the buses were fired at from inside Egyptian territory.
"The border is heavily guarded," said the Sinai-based official who spoke on condition of anonymity because he was not authorized to speak to the media.
Israel Radio said a vehicle had followed the first bus, and two to three gunmen got out and opened automatic weapons fire.
The vehicle carrying the assailants fled the scene, and Israeli security forces were in pursuit, Israel Radio said. Channel 2 said two helicopters had been deployed to join the chase.
TV footage showed the bus pulled over by a red rocky cliff. Windows and a door of the bus were shattered, and soldiers were patrolling the area on foot.
Inside the bus, seats were stained with blood and luggage littered the aisle.
"I was talking to someone sitting next to me and we heard gunshots and we immediately bent over and then we realized there were people injured," a young woman riding the bus told Channel 2 TV. She did not give her name.
The bus driver interviewed by Channel 2 did not provide details of the attack but appeared calm, smoking a cigarette in the driver's seat.