Most Revd Justin Welby was responding to Saturday night's shootings in Copenhagen which left two people dead, the killing of 21 Coptic Christians by IS in Libya and a number of suicide bomb attacks in Nigeria.
"The terrible cruelty of the murders in Denmark, Libya and Nigeria call for deep compassion for the bereaved and killed. 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," he said.
A video has been released by Islamic State claiming to show the beheading of 21 Coptic Egyptian Christians held in Libya.
Archbishop Justin added: "In Egypt and Libya, the home of Christian faith, of saints and martyrs since the earliest centuries, more suffering has been perpetrated.
"The Coptic church has responded with courage and as always with faith. The darkness which ISIS seek to spread will be overwhelmed by the faithful lives of Christians shedding the light and peace of Christ.
"I have been in touch with the Anglican Church in Egypt to express solidarity.
"Let us pray for the triumphant peace of Christ to be evident, and for governments affected to be wise and courageous."