At least 25 people have died and dozens more have been injured after a bomb exploded at Cairo's largest Coptic cathedral in the deadliest attack on the Christian minority in years.

The blast was detonated at 10:00 local time (08:00 GMT) on Sunday and struck the side of the church used by women and children. The incident, which happened on the Prophet Mohammed's birthday, caused waves of anger across Egypt as hundreds of Christians and Muslims gathered to protest outside St Mark's Cathedral.

The crowd demanded Magdy Abdel Ghaffar, the interior minister, be dismissed after a perceived security failure led to the attack. Christians are convinced attacks on them are not seriously investigated. 

"The Ministry of Interior cannot protect our churches. It is time for us to protect ourselves," said one protester. Others demanded the fall of the regime.

The attack comes as President Abdel Fattah al-Sisi fights battles on several fronts. A bloody crackdown on the Muslim Brotherhood has seen thousands jailed, while an insurgency rages in Northern Sinai, led by the Egyptian branch of ISIS.

The militant group has also carried out deadly attacks in Cairo and has urged its supporters to launch attacks around the world in recent weeks as it goes on the defensive in its Iraqi and Syrian strongholds.

There was no immediate claim of responsibility, but exiled Brotherhood officials and home-grown militant groups condemned the attack as ISIS supporters celebrated on social media.

The attack took place in a chapel that adjoins St Mark's, Cairo's main cathedral and the home of Coptic Pope Tawadros II, where security is normally tight. 

Coptic Christians make up about 10 per cent of Egpyt's population and face discrimination and persecution. 

As the largest Christian community in the Middle East, many 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 church.

The last major attack on a church took place as worshippers left a New Year's service in Alexandria weeks before the start of the 2011 uprising. At least 21 people were killed.

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.

The attack came two days after six police were killed in two bomb attacks, one of them claimed by Hasm, a recently-emerged group the government says is linked to the Muslim Brotherhood, which has been banned under Sisi as a terrorist organisation.

The Brotherhood says it is peaceful. Several exiled Brotherhood officials condemned the bombing, as did Hasm and Liwaa' al-Thawra, another local militant group.

Coptic Pope Tawadros II cut short a visit to Greece after learning of the attack. Church officials said they would not allow the bombing to create sectarian differences.

Bishop Angaelos, General Bishop of the Coptic Orthodox Church in the United Kingdom said he heard the news "with great sadness". 

He said he was praying for those whose lives had "so senselessy ended" and for their families and friends. 

In a statement on Sunday he said: "We also pray for every Coptic parish and community across Egypt as they fill their churches this morning, as well as for the broader Egyptian society that fall victim to similar inhumane attacks."

He added: "We share in this tragedy but are encouraged by the strength and resilience of our brethren in Egypt that we have grown accustomed to and learn from. We pray God's peace and protection upon the Christians of Egypt, the broader Egyptian society, Christians around the world worshipping this morning and all faith communities that fall prey to similar attacks."

At the Vatican, Pope Francis condemned what he called the latest in a series of "brutal terrorist attacks" and said he was praying for the dead and wounded. 

Sources said the explosion was caused by a device containing at least 12 kg (26 pounds) of TNT.

Police and armored vehicles rushed to the area, as hundreds of protesters gathered outside the compound demanding revenge for the attack that took place on a Muslim holiday marking the Prophet Mohammad's birthday and weeks before Christmas. Scuffles broke out with police.

A woman sitting near the cathedral in traditional long robes shouted, "kill them, kill the terrorists, what are you waiting for? ... Why are you leaving them to bomb our homes?"

Though Egypt's Coptic Christians have traditionally been supporters of the government, angry crowds turned their ire against Sisi, saying his government had failed to protect them.

"As long as Egyptian blood is cheap, down, down with any president," they chanted. Others chanted "the people demand the fall of the regime", the rallying cry of the 2011 uprising that helped end Hosni Mubarak's 30-year rule.

Sisi's office condemned what it described as a terrorist attack, declaring three days of mourning and promising justice. Al-Azhar, Egypt's main Islamic center of learning, also denounced the attacks. 

Additional reporting from Reuters.