Khaled Musaid and Tulub Murdi Suleiman were killed on Wednesday night in an exchange of fire with police in the Mount Halal area of the Sinai peninsula, near where another suspect, Moussa Badran, had been shot dead earlier in the day.
Younes Mohamed Mahmoud Alyan, who was driving the car the men were in, was arrested and has confessed to carrying out the Sharm el-Sheikh bombings, the ministry said in a statement on Thursday.
In the car, police found a video camera and tape recorded before the Sharm el-Sheikh attacks in which members of the group explained their roles. It also showed how an August attack that damaged a multinational observer force vehicle was carried out.
Police also found ammunition, a bomb, a locally made timer and false number plates.
Musaid, born in 1972, and Suleiman, born in 1982, both came from El Arish, a town on Sinai's Mediterranean coast that has been a focus for investigations since bombers attacked Taba and other nearby Sinai resorts in October last year.
Salem, who was married and had three young children, used to work as a dentist in El Arish hospital, the police officer said.
Egyptian police have arrested
scores of blast suspects
The Mount Halal area, where the two men were killed, lies about 60 km south of El Arish. Police had been tracking their vehicle before the gunfight. One police officer and three other members of the security forces were injured.
The Egyptian authorities have said they believe the same group was behind the Sharm el-Sheikh bombings, the Taba attacks and the August blast that damaged the observer vehicle.
They say the bombers are Sinai bedouin, some of them with Palestinian connections. The government says it has not seen any evidence that they are affiliated with any larger group.
Last month, a roadside bomb blasted a vehicle of the Multinational Force and Observers group in the region. The force of 1800 personnel monitors the 1979 Egypt-Israeli peace treaty.
And thousands of Egyptian security forces carried out a sweep in Sinai, detaining more than 700 people in connection with the attacks. Many have been released. It is not known if any have been charged.