The gesture comes as leaders are gathering in Crete for the Pan-Orthodox Council that begins on Sunday.
However, the Russian Orthodox Church has indicated that it will not be attending the historic meeting.
But Patriarch Kirill has clarified that he does not want disputes among Orthodox churches to "bring division and trouble into our ranks."
The religious leader has asked that all Church leader decisions are respected by all, whether they attend or not.
The Russian Patriarch claimed in a statement published by the Russian Orthodox Church that the meeting "can become an important step toward overcoming the present differences."
Patriarch Kirill wrote: "Brothers, we all are the one Body of Christ (cf. 1 Cor. 12:27).
"We have received the priceless gift of unity from the Lord and our Saviour Jesus Christ Himself.
"To preserve this gift is one of our principal tasks; it is a direct commandment of our Saviour' (Jn. 17:21)."
He concluded: "We assure you that our prayers will be with you in the days of the work ahead of you."
