Police and gunmen traded fire in the Sinai town of El-Arish on Thursday as security forces pushed ahead with a campaign aimed at quelling a surge in Islamist militancy, state television reported.
The state-owned Nile News television reported clashes outside a police station in the north Sinai town a day after reported air strikes killed 20 militants in a neighbouring village.
The campaign to uproot the militants was launched on Tuesday, two days after gunmen ambushed a border guard outpost near the border with Israel and killed 16 soldiers, the military said in a statement on Wednesday.
"Elements from the armed forces and interior ministry supported by the air force began a plan to restore security by pursuing and targeting armed terrorist elements in Sinai, and it has accomplished this task with complete success," it said.
Wednesday's reported air strikes in Tumah village - the first in the peninsula for decades - came as security forces massed near Rafah on the Gaza border for what they called a decisive confrontation with the militants.
A senior military official in Sinai confirmed the state television report and said '20 terrorists were killed' in Apache helicopter raids and when soldiers from the 2nd Infantry Division stormed Tumah.
He said the militants were trying to escape when the helicopter targeted their vehicles.
Other security officials in the north of the peninsula reported air strikes near the town of Sheikh Zuwayid, close to the village.
The fallout from Sunday's attack, the deadliest for Egyptian troops in decades, spread to Cairo where President Mohamed Morsi sacked his intelligence chief and two generals.
Morsi's opponents have used the deadly Sinai incident to attack the Islamist president, whose Muslim Brotherhood has good relations with the Hamas rulers of the Gaza Strip.