The attack in a village named Tumah, the first time the military has used air strikes in Sinai for decades, came as security forces massed near the Rafah border town for what they called a decisive confrontation with the militants.
A senior military official in Sinai, who spoke to reporters on condition of anonymity, said “20 terrorists were killed” in Apache helicopter air strikes and when soldiers with the 2nd Infantry Division stormed Tumah.
“The operation is continuing,” he said. Other security officials in the north of Sinai reported air strikes near the town of Sheikh Zuwayid, close to the village.
Overnight, unknown assailants attacked security checkpoints near the town of El-Arish, the officials said, adding that no one was killed in the confrontation.
The air strikes came a day after the military held a funeral for the 16 soldiers killed on Sunday’s attack by militants amid widespread calls for vengeance.
The soldiers were killed when Islamist militants raided a border guard base under the cover of mortar fire, and comandeered a military vehicle into neighbouring Israel before they were stopped by an Israeli helicopter strike.
Security forces had raided homes on Tuesday in search of suspects in the attack, as they prepared to close tunnels to the Palestinian Gaza Strip used to smuggle weapons and militants as well as food and other supplies.
Israel had handed over to Egypt six “completely charred” bodies that were in the armoured personnel carrier that was driven into Israel before being destroyed, said a medical official in El-Arish.
The bodies have not yet been identified. But security officials blame Bedouin militants and Palestinian Islamists from Gaza for the attack.
Sunday’s bloodshed highlighted the government’s tenuous grip on the Sinai Peninsula, from where Islamist militants have launched several rocket attacks on Israel and a deadly cross border raid last year.
It also presents a challenge to Egypt’s new Islamist President Mohamed Morsi, whose Muslim Brotherhood has good relations with the Hamas rulers of the Gaza Strip.
Morsi did not attend the funeral, where some protesters chanted slogans against the Brotherhood, and according to witnesses, tried to assault the Islamist Prime Minister Hisham Qandil.
His spokesman said in a statement that Morsi did not attend because the security measures needed to guard the president would have impinged on the “popular character” of the ceremony.
Morsi has received both Hamas’s chief and its prime minister in Gaza, Ismail Haniya, in visits, along with Palestinian president Mahmud Abbas, and his government had eased border restrictions on Gaza.
Following Sunday’s attack, Egypt closed until further notice its Rafah crossing with Gaza, the Palestinian territory’s only access to the outside world that is not controlled by Israel.
The enclave has been under a semi-blockade by Israel since Hamas seized it in 2007.
After president Hosni Mubarak’s ouster in February 2011, militants stepped up attacks in Sinai, prompting the military, then in charge of the country, to send reinforcements to the peninsula.