At least 36 people were killed and more than 100 injured in bomb attacks on two Coptic churches on Palm Sunday, in the latest assault on a religious minority increasingly targeted by Islamist militants.

There was no immediate claim of responsibility for the attacks, which come a week before Coptic Easter and in the same month that Pope Francis is scheduled to visit Egypt.

The first bombing, in Tanta, a Nile Delta city less than 100 kilometres outside Cairo, killed at least 25 and injured at least 78, Egypt's Ministry of Health said.

The second, carried out just a few hours later by a suicide bomber in Alexandria, hit the historic seat of the Coptic Pope, killing 11, including three police officers, and injuring 35, the ministry added.

Pope Tawadros, who had attended mass at Saint Mark's Cathedral, was still in the building at the time of the explosion but was not harmed, the Ministry of Interior said.

The bombings come as Islamic State's branch in Egypt appears to be stepping up attacks and threats against Christians.

In February, Christian families and students fled Egypt's North Sinai province after a spate of targeted killings.

Those attacks came after one of the deadliest on Egypt's Christian minority, when a suicide bomber hit its largest Coptic cathedral, killing at least 25. Islamic State later claimed responsibility for the attack.

Thousands gathered outside the church in Tanta shortly after the blast, some wearing black, crying, and describing a scene of carnage.

"There was blood all over the floor and body parts scattered," said a Christian woman who was inside the church.

"There was a huge explosion in the hall. Fire and smoke filled the room and the injuries were extremely severe," another Christian woman, Vivian Fareeg, said.

President Abdel Fattah al-Sisi and Prime Minister Sherif Ismail are set to visit the Tanta site on Sunday and Sisi has ordered an emergency national defence council meeting, state news reported.

'WE FEEL TARGETED'

A shift in Islamic State's tactics, which has waged a low-level conflict for years in the Sinai peninsula against soldiers and police, to targeting Christian civilians and broadening its reach into Egypt's mainland is a potential turning point in a country trying to prevent a provincial insurgency from spiralling into wider sectarian bloodshed.

Egypt's Christian community has felt increasingly insecure since Islamic State spread through Iraq and Syria in 2014, ruthlessly targeting religious minorities. In 2015, 21 Egyptian Christians working in Libya were killed by Islamic State.

"Of course we feel targeted, there was a bomb here about a week ago but it was dismantled. There's no security," said another Christian woman in Tanta referring to an attack earlier this month near a police training centre that killed one policeman and injured 15..

Copts face regular attacks by Muslim neighbours, who burn their homes and churches in poor rural areas, usually in anger over an inter-faith romance or the construction of a church.