Eleven people were killed when an explosion struck outside St Mark's Coptic Church in Alexandria, state-owned Nile News TV reported.
Pope Tawadros II, head of the Coptic Church, had been attending mass inside.
Twenty-five people had died in an earlier blast at St George's Coptic church, in the city of Tanta, about 130km (80 miles) south-east.
According to state media, Pope Tawadros is unhurt. His secretary said the attack in Alexandria was carried out by a suicide bomber who struck outside the church.
After the first explosion in Tanta, provincial governor Ahmad Deif told the state-run Nile News channel: "Either a bomb was planted or someone blew himself up."
General Tarek Atiya, a spokesperson at Egypt's interior ministry, told AFP news agency that the blast in Tanta took place near the altar.
A search is under way for any more explosives which could be in the vicinity.
The blasts appear to have been timed for maximum impact, as people gathered to mark Palm Sunday.
Egyptian security forces had been put on alert in anticipation of attacks.
Pope Francis, who is due to visit Egypt later this month, has condemned the attack.
In December last year, 25 people died when a bomb exploded at the Coptic cathedral in Cairo during a service.
And in February, terrorists from the ISIS group warned of more attacks against Copts, who make up about 10% of Egypt's population.
The explosion occurred as Coptic Christians were celebrating Palm Sunday, one of the holiest days in the Christian calendar, marking the triumphal entry of Jesus Christ into Jerusalem.
On 1 April, an explosion outside a police training centre in Tanta injured 16 people.
