Police launched an attack on a group of militants in an under-construction shelter in Al-Arish city, killing six of them, the Interior Ministry said in a statement.
They were planning a series of attacks against police in the coming days, it said.
In a separate incident, the army killed two terrorists and arrested two others while they were preparing for an attack against military in North Sinai.
A number of suspected terrorists have also been arrested.
The raids by police and army came days before 'National Police Day' which marks the anniversary of Egypt's 2011 uprising that toppled former president Hosni Mubarak.
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The attacks, targeting police and military, increased after the ouster of Islamist ex-president Mohamed Morsi in 2013 by military following massive protests against his rule.
Hundreds of police and army personnel have been killed since then.
The military has launched security campaigns in North Sinai where some terrorists are based. They have arrested suspects and demolished terrorists' den, including those facilitating tunnels leading to the Gaza Strip.