It covers north and central Sinai, the Nile Delta and the Western Desert along the porous border with Libya.
A total of 16 militants were killed, it added.
The attacks, mainly targeting police and military, increased after the ouster of Islamist ex-president Mohamed Morsi in 2013 by military following massive protests against his rule.
In remarks to "Ten new" talk show on TEN channel on Friday evening, Radi said that "Sinai 2018 is a result of a series of military efforts and investigations since 2013, and particularly after the Rawdah Mosque attack", which occurred on November 24, 2017 and claimed lives of more than 300 people in North Sinai.
The authenticity and date of the 23-minute video could not immediately be verified, but a reference to an Egyptian military statement on Friday suggested that at least part of it was completed after the security operation began.
Suspicion for that attack fell on an affiliate of the Islamic State (IS) group in Sinai and Mr Sisi authorised troops to use "all brute force" necessary to restore "security and stability" to the region within three months.
Security forces also uncovered and destroyed six farms used to grow banned narcotics, the statement said.
Hundreds of police and army personnel were killed since then.
"Thus, they (the operations) are based on previous success against the terrorist groups in Sinai, so it has turned now to be carried out on large-scale", Radi said, noting that President Abdel Fatah al-Sisi is following up the operation.
The footage highlights the Egyptian military's top-of-the-line weaponry, including French Rafale fighters, US F-16 fighter-bombers, US Apache attack helicopters, a modern EADS transport aircraft, the Casa C-295, and US twin-rotored Chinook helicopters.
The comprehensive anti-terror operation "Sinai 2018" comes weeks before Egypt starts its 2018 presidential elections scheduled for late March, where incumbent President Sisi is expected to make an easy win for a second term due to the lack of strong challengers in the race.