Egyptian security officials said helicopters attacked militant strongholds in the city of Sheikh Zuweid on Friday, reports say.
Government spokesmen have said they intend to "fully cleanse" the area of militants.
Military sources say 22,000 soldiers have been deployed to help bring this about, adding that the campaign will take at least six months.
In another development, Egyptian security forces have foiled a terror attack on ships crossing the Suez Canal.
The extremist Salafist group Ansar Bayt al-Maqdis planned to attach vessels with RPGs, but Egyptian armed forces could avoid the terrorist act, local media outlets reported.
Last month, Egyptian officials said they foiled another attack on a container ship which was aimed at disrupting shipping in the busy Suez Canal.
Canal authority head Mohab Mamish said a "terrorist element" targeted a Panama-flagged vessel on August 31, but it was undamaged.
The Suez Canal - between Port Said and Suez - is a vital global trade route between the Red Sea and Mediterranean.
NTJ/BA