Most of the casualties were in the provincial capital, El-Arish.
Militant group Sinai Province, which changed its name from Ansar Beit al-Maqdis when it pledged allegiance to Islamic State, said it carried out the “extensive, simultaneous” attacks.
The hardline Sunni militant group has seized swathes of Iraq and Syria, drawing U.S.-led airstrikes.
Egypt’s president cut short a visit to Ethiopia because of the attacks.
They represent some of the worst anti-government violence in Egypt for months, and indicate a previously unseen level of co-ordination, correspondents and analysts said.
The flagship government newspaper, al-Ahram, said its office in the city of Al-Arish, which is situated opposite the military buildings, had been “completely destroyed,” although it was not clear if it had been a target.
Later, suspected militants killed an army major and wounded six others at a checkpoint in Rafah, while an assault on a checkpoint south of Al-Arish wounded four soldiers, security sources said. A roadside bomb in Suez city, not in the Sinai, that killed a police officer was not claimed by IS.
Tensions have also been raised across Egypt this week amid protests marking the anniversary of the 2011 uprising that ousted then-leader Hosni Mubarak.
Security officials said rockets were first fired at police offices, a military base and a military hotel in El-Arish, before a car bomb exploded at the rear gate of the military base.
More than 50 people were wounded in Thursday’s attacks.
North Sinai has been under a state of emergency and a curfew since October, when an attack on a checkpoint killed dozens of soldiers.
The army has launched major operations to try to quell violence in the region, but has so far failed.
Sinai Province has become the biggest threat, staging many attacks on security targets.
President Sisi is the former military chief who led the crackdown on Mr Morsi’s Muslim Brotherhood. The Brotherhood has said it rejects violence.
Egypt is creating a 1km (0.6-mile) buffer zone along the border with Gaza in a bid to stop militants smuggling weapons in from the Palestinian territory using tunnels.
The project has displaced more than 1,000 families in Rafah and severed an economic lifeline for many Palestinians.
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