Egypt's army said it killed 27 militants in the latter stages of a second day of a major operation it began on Monday to eliminate insurgents in volatile North Sinai, bringing the death toll to 56.

The army said 154 suspected militants have now been arrested by troops and anti-terror police backed up by air support.

Operation Martyr's Right was launched on Monday morning to "root out terrorist elements" in the North Sinai towns of Rafah, Arish and Sheikh Zuweid, in what sources described as the biggest operation of recent months.

Earlier on Tuesday the military said forces had killed 29 "terrorist elements" as it began the "comprehensive operation." It said an army officer and a soldier were also killed, and four wounded, when their armoured vehicle drove over a bomb.

A subsequent statement late on Tuesday said another 27 had been killed, driving the toll up to 56 in two days. It added that forces burnt out several terrorist "dens" and destroyed two explosives caches and tens of motorbikes and other vehicles used by militants in terrorist operations.

It also released a three-minute video documenting air and ground assaults on targets in the northern part of the Sinai Peninsula.

Islamist militant group Ansar Beit Al-Maqdis, the Egyptian Islamic State-affiliate that has intensified attacks on army and police personnel since the 2013 ouster of Islamist president Mohamed Morsi, has claimed responsibility for most anti-state attacks in Egypt's North Sinai.

The group said it killed the two soldiers on Monday with a roadside bomb that blew up their armoured vehicle as it left a military base in a large convoy.

The Egyptian military began an intensive security sweep of the region in August 2012 after an attack killed 16 Egyptian soldiers, at the time the deadliest internal attack on Egyptian troops in years.

Troops have since been struggling to crush an Islamist insurgency that has left hundreds of army and police personnel in Sinai and on the mainland dead.

Last week six peacekeepers, including four Americans, with a multinational force monitoring Egypt's peace treaty with Israel were injured in two bomb attacks.