The fiercely anti-Israeli group Al-Salafi al-Jihadiya, in a statement posted on Islamist forums, condemned "the state media and the army as liars" who "celebrate fake victories in the Sinai".
Yesterday, the military launched what security sources said was its "biggest" air assault on Sinai where the army has been battling a semi-insurgency since Islamist president Mohamed Morsi's ouster on July 3.
The strikes near the Rafah crossing into Gaza targeted militants using the area bordering the Palestinian territory as a hideout, the sources said.
The jihadist group denied the claims.
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"The operation has seen innocents being arrested and presented as fighters," the group said.
"They film the bombing of homes and present them as dens of fighters and openly lie about the deaths of large numbers of" militants, it added.
The security sources said the air assault also targeted weapons depots and explosives, apart from militants hiding in villages.
Egypt has deployed additional forces to fight radical groups in the mainly desert region.
On August 19, militants killed 25 Egyptian police in an attack on two buses heading towards the town of Rafah.
Many radical groups have set up rear bases in northern Sinai, a region mostly populated by Bedouins who are themselves often in conflict with the central authorities in Cairo.