The violence erupted when security forces raided the hideouts of the militants in al-Goura village in Sheikh Zoweid area in the northern Sinai region that borders Israel and the Gaza Strip, Egyptian media reported.
The bodies of those militants killed and the wounded were taken to the el-Arish Hospital, they said.
The militants possessed rocket-propelled grenades, automatic guns and a large number of hand grenades, security sources said, adding they had exchanged fire with the army.
The fresh violence comes days after the start of a military operation in the region against militants who killed 16 Egyptian soldiers last Sunday.
Today's clashes took place after armed men attacked several Egyptian army checkpoints.
The Al-Ahram website reported that armed men fired on a checkpoint near the eastern entrance to Sheikh Zuwayed, on the Rafah-Arish international road. Eight armed men fired on another army position on the Arish-Ouja road.
Quoting eyewitnesses it said army forces exchanged fire with the assailants before they fled into a nearby mountainous area after reinforcements arrived.
In a separate incident, three policemen were killed and four others injured when their car overturned while chasing suspected militants on the international road in central Sinai, state-run news agency MENA reported.
Egypt sent hundreds of troops and armored vehicles into northern Sinai to tackle militants operating near the border in an offensive that commanders said has so far killed 20 people. PTI