The Archbishop of Canterbury has condemned the "terrible cruelty" of the murder of 21 Coptic Christians in Libya, as well as the killings in Denmark and Nigeria over the weekend.

In a statement from Lambeth Palace, the Archbishop said: "The killers seem to rejoice in ever more extreme acts carried out to inflict ever greater terror. We must all weep with those affected, and know that in the love of Christ all evil will be overcome."

Referring to Egypt and Libya as "the home of Christian faith," Justin Welby praised the Coptic Church for responding with courage and faith to the most recent atrocity.

"The light and peace of Christ are at the heart of the faithful lives of Christians, and will not be overcome by the darkness which ISIS seek to spread," he said, adding that he has personally expressed solidarity with the Anglican Church in Egypt.

"Let us pray for the peace of Christ to be evident, and for governments affected to be wise and courageous."

Islamic State issued a video on Sunday purporting to show the beheading of 21 Egyptian Christian men kidnapped in Libya.

The five-minute video is titled: "A message signed with blood to the nation of the cross" and the men are identified as "people of the cross, the followers of the hostile Egyptian Church."

In a message to the "crusaders", a masked insurgent holding a knife says his fellow militants are "chopping off the heads of those that have been carrying the cross illusion."

UK Foreign Secretary Philip Hammond has strongly condemned the murders.

"Such barbaric acts strengthen our determination to work with our partners to counter the expanding terrorist threat to Libya and the region. Acts of terrorism should not be allowed to undermine Libya's political transition," Hammond said today.

"We remain fully supportive of the UN's efforts to build a national unity government for Libya and to bring a political solution to the ongoing security crisis. Those who support terrorists can have no part in this process."

Egyptian President Abdel Fattah al-Sisi has called a seven-day mourning period, and state television reported that the military had carried out an air strike against IS targets in Libya at dawn on Monday.

On Saturday, two people were killed by a gunman in Copenhagen, who is thought to have been inspired by the January attack on French satirical magazine Charlie Hebdo.

In Nigeria, a female suicide bomber killed ten people and wounded at least 30 in an explosion at a crowded bus station in the northeast city of Damaturu on Sunday. No group has yet claimed responsibility for the attack, but it is thought to have been perpetrated by Islamist militant group Boko Haram.