The clergyman, named as Fr Samaan Shehta, was struck on the head with the knife in the suburb of El-Marg on Thursday.
In a statement, General Bishop of the Coptic Orthodox Church in the UK Bishop Angaelos spoke of his anger, saying: "Another day in Egypt with another Coptic Christian murdered".
His Grace continued: "I am sure that I am not alone in my anger, but that it is shared by every law-abiding person of any belief and indeed of none, who has witnessed this vicious and inhumane attack."
Coptic leaders report that Fr Samaan had travelled from Beni Suef in Upper Egypt to Cairo (pictured below) to collect humanitarian aid for people in his parish.
Security officials are yet to establish a motive behind his death. They say a man who fled the scene has since been arrested.
The death of Fr Samaan Shehta is the latest in a line of deadly assaults in recent month on Egypt's Christian minority - which account for ten per cent of the country's population.
Bishop Angaelos commented: "Coptic Christians - who have endured injustice, persecution, and loss of life for centuries without retaliation, repeatedly forgiving unconditionally - deserve to live with respect and dignity in their indigenous homeland."
A spate of suicide bombings claimed by the extremist Islamic State group has killed more than 100 people since December last year.
Click here to listen to Premier's Alex Williams speaking with Bishop Angaelos: