He sent a message to Pope Tawadros II of Alexandria after they met in Rome two years ago.
The Coptic Church is the largest community of Christians in the Middle East.
The Pope wrote: "Today more than ever we are united by the ecumenism of blood, which further encourages us on the path towards peace and reconciliation.
"I assure you and the Christian community in Egypt and throughout the Middle East of my unceasing prayer."
He added: "Christians throughout the world are facing similar challenges, which require us to work together in confronting these issues.
"I appreciate your appointment last year of a delegate to participate in the Extraordinary Synod of Bishops dedicated to the family.
"It is my hope that our cooperation in this area may continue, especially in addressing matters related to mixed marriages.
"With these sentiments, and recalling what has rightly become known as the day of friendship between the Coptic Orthodox Church and the Catholic Church, I exchange with Your Holiness a fraternal embrace in Christ the Lord."
