"Terrorist elements targeted a checkpoint west of El-Arish early this morning... The exchange of fire killed five terrorist elements and eight police were martyred," an interior ministry statement said.
Some militants escaped and security forces are following "their movements", the ministry added.
A security source said reinforcements had been dispatched to the checkpoint near El-Arish, capital of North Sinai province.
"The checkpoint is currently surrounded by the army and police," he said.
Three members of the Central Security Force, under the control of the interior ministry, were also wounded in the attack and taken to El-Arish public hospital, a medical source said.
Egyptian state television said there were fears the death toll could rise amid reports of attacks on multiple checkpoints. It broadcast still images it said were of the slain attackers.
Egypt has for years been battling insurgents in the North Sinai affiliated with the Islamic State group.
Hundreds of police officers and soldiers have been killed in attacks which surged after the army's ouster of president Mohamed Morsi in 2013 by general turned president Abdel Fattah al-Sisi.
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