Sisi announced the "state of emergency for three months" in a defiant speech at the presidential palace after a meeting of the national defence council.
The Islamic State group had claimed responsibility for the church bombings in the Nile Delta cities of Alexandria and Tanta in which at least 44 people were killed.
The emergency law expands police powers of arrest, surveillance and seizures and can limit freedom of movement.
Egypt had been ruled for decades under a state of emergency, which was cancelled a month before Islamist president Mohamed Morsi took power in 2012.
Rescinding it had been a main demand of Egyptian rights activists during the 2011 revolt that overthrew veteran strongman Hosni Mubarak.
Following Morsi's overthrow by Sisi, then an army chief, in 2013, a state of emergency was declared for a month after deadly clashes between police and Islamist protesters killed hundreds and Islamist mobs attacked Christian properties.
Part of North Sinai where the Islamic State group's Egyptian affiliate is based has remained under a state of emergency.
Footage of the explosions
Egypt's Interior Ministry has published footage captured by CCTV cameras showing the moment a suspected suicide bomber attacked a Coptic cathedral in Alexandria Sunday, Reuters reports.
The bomber, wearing a brown jacket with a blue sweater tied over his shoulders, is seen walking up to the cathedral's gate and is refused entry. He then walked to a metal detector at the gate's entrance before an explosion erupted.
Egypt's Ministry of Health said 16 people were killed, including three police officers, and 41 injured.
The explosion came just hours after a bombing rocked a Coptic church in Tanta, killing at least 27 people and injuring 78. Meanwhile, other video footage emerged on Twitter purporting to be of the moment leading up to the blast in the Mari Girgis church in Tanta, also on Sunday: