Ten jihadists have been killed in Egypt's restive Sinai peninsula in the past two days during an army offensive against Islamist militants, the official MENA news agency reported on Thursday.

"The security operation carried out by the armed forces in northern Sinai in the past 48 hours led to the deaths of 10 jihadists," a military source was quoted as saying.

The report comes hours after militants killed three Egyptian policemen in separate overnight attacks in the region, and as the army pressed an operation to curtail a surge in violence since the ouster by the army of president Mohamed Morsi on July 3.

Three unknown gunmen attacked a police station in the town of Sheikh Zuweid, wounding three policemen in a gun battle before fleeing in their vehicle, medical and security officials said.

One of the wounded, identified by the state news agency as police officer Mohamed Said Metwali, 34, died at the El-Arish hospital shortly afterwards.

Another policeman was shot dead by gunmen outside his home in El-Arish, the main town in north Sinai.

Late on Wednesday, militants also opened fire on a police station in El-Arish, the officials said, killing a police conscript who was standing guard outside the building, before fleeing in their vehicle.

And on Tuesday, militants fired rocket-propelled grenades at a checkpoint in the border town of Rafah, wounding six police and two civilians, security sources said.

The wave of attacks in Sinai came as Egyptian military reinforcements arrived in the increasingly lawless region, which borders Gaza, after Israel gave Egypt the go-ahead to deploy two battalions to the region to "fight terrorism".

Deployments in the Sinai are restricted by the 1979 peace treaty between the two neighbours.

Since the military coup that toppled Morsi after massive nationwide protests against his rule, militant groups have launched almost daily attacks on troops and police in Sinai.

Several members of the security forces have died in the unrest, as well as two Egyptian Christians, one of whom was found decapitated five days after being kidnapped.

At dawn on Monday, three workers from a cement factory were killed in an attack on the bus in which they were travelling in El-Arish.

Analysts attribute the Sinai violence to Islamist extremists seeking to take advantage of the political insecurity in the country after Morsi's removal.