The Islamist militants have increasingly shifted their campaign from the restless Sinai Peninsula to the capital and other Nile Delta areas, with bombing and shooting attacks on security forces.
In the early morning raid north of Cairo, five jihadists with the Al-Qaeda-inspired Ansar Beit al-Maqdis group were also killed in the hours-long shootout, the interior ministry said.
The group has claimed responsibility for some of the deadliest attacks in a low-level insurgency that has killed more than 200 policemen and soldiers since the army overthrew Islamist president Mohamed Morsi in July.
They were hiding out near the Nile Delta town Al-Qanatir Al-Khayriya, roughly 30 kilometres (19 miles) north of Cairo.
The officers killed in the raid were bomb disposal experts who participated in the operation alongside police, the military said.
It said "a large quantity of explosives" was found in the hideout, with the interior ministry saying militants had used explosive belts during the confrontation.
Most of the attacks following Morsi's overthrow have taken place in the lawless Sinai Peninsula, where jihadist leaders are believed to be based.
The group said last week that its founder, Tawfiq Mohamed Fareej, was killed recently when a car accident set off a bomb he was carrying.
Fareej was the "field commander" of an August 18, 2011 cross-border raid into Israel that killed eight Israelis, the group said.
He was involved in the failed assassination of the interior minister in September.
The group also acknowledged the death of one of its militants in a shootout with police in Cairo earlier in the month.
Several new militant groups have cropped up amid a deadly security crackdown on Morsi's supporters, which has killed at least 1,400 people, according to Amnesty International.
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