Images have been posted on social media showing knives being held to the men's throats with the slogan "the humiliated followers of the Coptic Church".
A video has also been released appearing to show the men being beheaded. At the end of the recording a militant said the group planned to "conquer Rome".
The Egyptian Foreign Ministry confirmed the deaths of the men who were kidnapped from the Libyan city of Sirte in the early hours of 3 January.
A second image showing the men in orange clothes has the title "Revenge for the Muslim women persecuted by Coptic crusaders in Egypt".
Bishop Angaelos General Bishop of the Coptic Orthodox Church in the United Kingdom said the men had been "brutally executed" and that he was "praying for them, their families and all remaining captives".
He added: "It is with deep feelings of sorrow and pain that we received confirmation of the brutal murder of Coptic Christians in Libya at the hands of Daesh (IS).
"While every life is sacred and every death tragic, the particular brutality demonstrated in this instance and others like it shows not only a disregard for life but a gross misunderstanding of its sanctity and equal value in every person.
"Our prayers are particularly with the families of these young Coptic men, who were fathers, brothers, sons and friends of many within their tight-knit rural communities, in which their absence will cause significant loss and sorrow.
"Their families are not only deprived of breadwinners who had travelled to Libya to support them, but of the joy that they bring when they return.
"While it may seem illogical or incomprehensible, we also pray for those who have carried out these horrific crimes, that the value of God's creation and human life may become more evident to them, and in this realisation, that the wider effects of pain brought by this and other acts of brutality may be realised and avoided."
Overnight Egypt has launched air strikes on IS targets in Libya in retaliation for the deaths.
Weapons caches and training camps were bombed to "avenge the bloodshed", military commanders said.
Listen to Bishop Angaelos on Premier's News Hour: