A military source told state TV the suspects in the Sunday attack are "terrorists" belonging to radical groups, the Egypt Independent reported.
The attack was followed by others in Egypt this week.
On Friday, gunmen riding motorbikes fired on a police station in the North Sinai governorate but no one was injured, police said.
The gunmen fled after the attack, which came hours after Bedouin leaders met with Egypt's new interior minister, Ahmed Gamal al-Din, to discuss ways to end the violence that has erupted recently, CNN reported.
The minister blamed the situation on tunnels between Egypt and Gaza, saying they were smuggling routes for terrorists and weapons.
"All tribal chiefs of Sinai agreed to the destruction of all tunnels," tribal leader Mohamed Tarabeeni told CNN. "The minister requested the assistance of the Bedouins in securing the region and protecting the borders the same way they did during the 1967 and 1973 wars with Israel."
In the Sunday attack, gunmen armed with semiautomatic weapons and hand grenades, stole two armored vehicles from Egyptian forces, then tried to enter Israel.
Egypt's military leadership said 35 assailants were involved in the attack near the Rafah border crossing from Gaza to Egypt.
An Egyptian general involved in intelligence in North Sinai told CNN it was likely those involved in Sunday's attacks "are members of Palestinian Islamic Jaljala Army, which is a group considered an offshoot of Hamas but with more radical beliefs."
Hamas, which controls Gaza, has denied the charge, calling the attack an "ugly crime."
A Palestinian Authority spokesman in Gaza said Hamas leaders decided to close the tunnels. On the Egyptian side, bulldozers and cranes were deployed to block the tunnels into Gaza.
On Wednesday, coordinated attacks across North Sinai led to clashes between militants and Egyptian security forces. North Sinai security officials reported some casualties.