Egypt has sent more troops and armoured vehicles to try to regain control of the Sinai peninsula, where fighting is escalating.
Sixteen guards at the border with Israel were killed on Sunday. Further attacks followed on checkpoints in al-Arish on Wednesday, which left a number of people wounded.
Missile strikes were launched from helicopters several hours later.
According to the Mena news agency, the army has also begun sealing off tunnels into Gaza.
The agency says there are more than 1200 illegal tunnels along the Egypt-Gaza border that are used for smuggling people and goods.
The BBC reports Sunday's attackers are believed to have used them as an escape route.
Egyptian state television says gunmen fired bullets at a police station in the main town in northern Sinai, El Arish.
But a security source told Mena the shots were fired into the air by a man driving an unlicensed car.