EILAT, Israel >> Gunmen who crossed from the Egyptian desert launched a series of attacks today in southern Israel, killing eight people and threatening to destabilize a volatile border region that includes the Hamas-ruled Gaza Strip and the increasingly lawless Sinai Peninsula.

Israel blamed an armed Palestinian group from neighboring Gaza. Israeli forces killed five of the gunmen along the border with Egypt, the military said, and later launched an airstrike inside Gaza that killed five other militants from the same group as well as a child.

The Israeli military said three of the men killed in Gaza had been involved in planning the attack.

Gunfire continued on both sides of the border late into the evening. After nightfall, Israel’s “Iron Dome” anti-missile system intercepted a rocket fired by Gaza militants at the city of Ashkelon, the military said.

The attacks were the deadliest against Israelis since a gunman killed eight civilians in Jerusalem in 2008. They suggested that Egypt’s recent political upheaval and a resulting power vacuum in Sinai had allowed militants to open a new front against Israel on the long-quiet frontier.

The attack began shortly after noon in southern Israel with gunfire at a civilian bus heading toward the Red Sea resort city of Eilat, currently at the height of the tourist season.

A number of passengers were hit, the military said. The gunmen had crossed the border and set up an ambush along a 300-yard strip, armed with automatic weapons, grenades and suicide bomb belts, according to the military.

“We heard a shot and saw a window explode. I didn’t really understand what was happening at first,” passenger Idan Kaner told Israel’s Channel 2 TV. “After another shot, there was chaos in the bus and everyone jumped on everyone else.”

Within an hour, gunmen had riddled another passing bus and two cars with bullets and rigged a roadside bomb that detonated under an army jeep rushing to the scene. At the same time, mortar gunners in Gaza opened fire at soldiers along the Gaza-Israel border fence.

TV video showed the first bus with its windows shattered. Its seats were stained with blood and luggage littered the aisle.

The Israeli dead included six civilians and one soldier, according to the Israeli military’s southern commander, Maj. Gen. Tal Russo.

Israeli soldiers eventually killed five attackers, the military said, and defense officials said three of the bodies were wired with explosives. It was not clear how many militants were involved or where they were from.

Egyptian security and Interior Ministry officials said a gunfight erupted on the border, and three Egyptians were killed, one police officer and two soldiers. The officials, speaking on condition of anonymity because they were not authorized to brief reporters, said the gunfire erupted while Israelis were chasing militants who were trying to re-enter Sinai. It was not clear if the gunfire at the Egyptians came from Israeli soldiers or the militants. The Israeli military had no comment.

According to the Israeli military, during the fighting along the border the gunmen tried and failed to shoot down an Israeli helicopter with an anti-tank missile.

Roadblocks were erected in the area, sealing roads in and out of Eilat, and senior Israeli security officials convened an emergency session at the Defense Ministry in Tel Aviv.

Hours later, militants who had apparently gone undetected attacked again, and a member of an elite police counter-terrorism unit was killed, the eighth Israeli fatality, according to Chief Inspector Alex Kagalsky, a spokesman for the Israel police.

Israel said the attackers had come from Gaza and made their way into neighboring Sinai and from there into Israel.

“Today we all witnessed an attempt to step up terror by attacking from Sinai. If anyone thinks Israel will live with that, he is mistaken,” Prime Minister Benjamin Netanyahu said late today. “If the terror organizations think they can strike at our civilians without a response, they will find that Israel will exact a price — a very heavy price.”

U.S. Secretary of State Hillary Rodham Clinton condemned what she called “premeditated acts of terrorism against innocent civilians,” and said the U.S. and Israel were “united in the fight against terror.”

Clinton added that the violence “only underscores our strong concerns about the security situation in the Sinai Peninsula,” and urged the Egyptian government to find “a lasting solution.”

The U.S. Embassy in Tel Aviv issued an “emergency message” urging U.S. citizens to avoid the area of the attack and requiring embassy employees and their families to receive approval before traveling to Israel’s south.

Taher Nunu, a spokesman for the Hamas government, denied the militants’ complicity, saying Gaza “has nothing to do with these attacks.”

The Israeli military said the attacks had been executed by a Hamas-linked group known as the Popular Resistance Committees, and that their objective had been to kidnap civilians or soldiers. The group was involved in the capture of an Israeli soldier, Sgt. Gilad Schalit, who has been held captive in Gaza for more than five years.

An Israeli airstrike on Gaza killed five members of the group, including its commander, as well as the 3-year-old child of one of the militants, according to Hamas security officials.

A spokesman for the Popular Resistance Committees, Abu Mujahid, would not comment on its alleged complicity. He threatened retaliation for the deaths of the group’s members.

Though it seemed clear the gunmen had come through Egyptian territory, Gen. Khaled Fouda, the governor of the southern Sinai district, said no shooting had come from the Egyptian side.

“The incident underscores the weak Egyptian hold on Sinai and the broadening of the activities of terrorists,” said Israeli Defense Minister Ehud Barak. “The real source of the terror is in Gaza, and we will act against them with full force and determination.”

The Sinai desert, dominated by Bedouin tribes and never entirely under the control of the central government, have grown more violent since a popular uprising toppled longtime Egyptian ruler Hosni Mubarak in February. Since then, assailants have repeatedly blown up a crucial pipeline carrying natural gas to Israel and Jordan.

Egypt moved thousands of troops into the area last week as part of a major operation against al-Qaida-inspired militants who have been increasingly active there since Mubarak’s ouster.

Most of the routine traffic across the remote, mountainous border involves Bedouin smugglers ferrying drugs and African asylum seekers into Israel.

There is a thriving smuggling trade between Sinai and Gaza through tunnels under the border, and goods and people can move in both directions. If the attackers were from Gaza, they could have reached Sinai through the tunnels and then crossed the Israel-Egypt border, which is largely unfenced, making their way toward Eilat, which is 130 miles (200 kilometers) from Gaza.