Pope Francis went on to laud the theological dialogue which has contributed to helping recover their unity before the Great Schism of A.D. 1054.
Addressing Metropolitan Methodius, who heads the Greek Orthodox Metropolis of Boston and led Tuesday's delegation, the Pope expressed his appreciation for his work as co-president of the North American Orthodox-Catholic Theological Consultation.
Instituted in 1965, "this Consultation has proposed significant reflections on central theological issues for our Churches, thus fostering the development of excellent relations between Catholics and Orthodox on that continent," he said.
The pontiff also looked ahead to September's Joint International Commission for Theological Dialogue between the Catholic Church and the Orthodox Church. "The task of this Commission is indeed precious; let us pray the Lord for the fruitfulness of its work."
Francis went on to recall meeting Bartholomew I and Athens archbishop Beatitude Ieronymos II during his April visit to Lesbos, where they met with some of the thousands of migrants and refugees who had landed on island.
"Seeing the despair on the faces of men, women and children uncertain of their future, listening helplessly as they related their experiences, and praying on the shore of the sea that has claimed the lives of so many innocent persons, was a tremendously moving experience," he said.
"It made clear how much still needs to be done to ensure dignity and justice for so many of our brothers and sisters."
The Pope said it was a "great consolation" to share the "sad experience" with the patriarch and archbishop.
"Led by the Holy Spirit, we are coming to realize ever more clearly that we, Catholics and Orthodox, have a shared responsibility towards those in need, based on our obedience to the one Gospel of Jesus Christ our Lord."
"Taking up this task together is a duty linked to the very credibility of our Christian identity. Consequently, I encourage every form of cooperation between Catholics and Orthodox in concrete undertakings in service to suffering humanity."
Acknowledging the Pan-Orthodox Council which recently concluded at Crete, Francis concluded: "May the Holy Spirit bring forth from this event abundant fruits for the good of the Church."
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In a letter addressed to Pope Francis to mark the solemnity of Saints Peter and Paul, Patriarch Bartholomew lauded the efforts which have been made toward unity between the Churches.
"Our endeavors are nurtured by this endless source for the advancement of the journey toward the desired unity of our Churches," he writes in the letter.
"The dialogue that continues between the Orthodox Church and the most holy Church of Rome is a domain that produces theological knowledge, ecumenical experience and mutual enrichment."
The ecumenical patriarch also addressed the role of the Church in honoring "honors humankind created in the image and likeness of God."
"This is why the word of the Church is and shall remain to the ages an intervention for the sake of humanity and its divinely-granted freedom."
"Life in the Church incorporates, along with the Holy Eucharist, the splendid worship and life of prayer, the ascetic and internal struggle against the passions, as well as the resistance against social evil and the struggle for the prevailing of justice and peace."