The Sinai border has been largely quiet for most of the three decades since Israel and Egypt signed a peace agreement, although security forces have for years combated a low-level insurgency in El-Arish and nearby areas. The 1979 treaty restricts the number of troops and the type of weapons Egypt can deploy in the peninsula.
Israel has agreed in the past to Egypt sending reinforcements to bolster its forces there, but the Egyptian officials did not say whether Israel had signed off on the helicopter deployment.
The officials spoke on condition of anonymity because they were not authorized to speak to the media.
Sinai's security problems have their roots in the resentment by its native Bedouins of what they see as the police's heavy-handedness and the lack of adequate government services. Security officials there say Islamists have forged alliances among some of the disgruntled Bedouins.
In Israel, Prime Minister Benjamin Netanyahu on Monday paid an unannounced visit to the site where the militants broke through, praising Israeli security forces for their swift response and expressing regret for the loss of the Egyptian lives.
"Israel and Egypt clearly have a shared interest in maintaining a quiet border," Netanyahu said. "But when talking about the security of Israeli citizens, Israel must and will rely only on itself," he added.
Other Israeli officials gave more details of the attack and their response.
Chief military spokesman Brig. Gen. Yoav Mordechai told Army Radio that after killing the soldiers, the militants seized a truck and an armored car, then blew up one of the vehicles to punch a hole through a security fence to enter Israel.
He said that Israeli intelligence services had reports of impending infiltration and sent aircraft to strike as the militants broke through. "We were prepared for it, so there was a hit," he said. The military "averted a major attack on southern Israel," he added.
The attack was the third cross-border infiltration since Mubarak's overthrow. In one, in August 2011, eight Israelis and six Egyptian soldiers were killed. The six Egyptians were mistakenly killed by Israeli forces. Israel is building a fence along the border to block militants as well as illegal African migrants, but also wants Egypt to crack down harder on the border region.
"We hope this will be a fitting wakeup call for the Egyptians to take things in hand on their side more forcefully," Defense Minister Ehud Barak told parliament's foreign affairs and defense committee on Monday. He said there were between six and eight militants killed.
Egypt-Israel relations have always been cool but since Mubarak was overthrown and Islamists rose to power, Israeli officials have expressed concern that ties would further deteriorate. Israel is particularly concerned that Egypt will ease restrictions on entering and leaving the Gaza Strip.
Immediately after the attack, Egypt shut the Rafah crossing with Gaza, an ominous sign for the Palestinian territory's 1.6 million people. Israel bars Gazans from entering Israel, so the Rafah crossing — the only exit from the tiny coastal territory not under direct Israeli control — is their sole gateway to the outside world.
Gaza officials disowned the attack but gave mixed signals over whether residents of the territory may have carried it out.
Gaza's deputy prime minister, Mohammed Awad of the ruling Hamas movement, said militants from the territory were "not involved in this awful crime." But a leading Hamas member, Mohammed Zahar, undercut that denial, telling Al-Jazeera TV that he asked Egypt to provide the names of possible suspects from Gaza so that "we will immediately bring them to justice."
The attack could harm Hamas' efforts to persuade Morsi to ease restrictions at the crossing. Hamas is an offshoot of the Muslim Brotherhood and had hoped that Morsi, a fellow member of the region-wide movement, would be sympathetic to its requests. But he has moved cautiously, in part because of concerns about an influx of militants from Gaza.
Teibel reported from Jerusalem. Associated Press reporters Ibrahim Barzak in Gaza City, Gaza Strip, and Mohammed Daraghmeh in Ramallah, West Bank, contributed to this report.
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