The Pope said this when he visited the headquarters of the Congregation for Eastern Churches on Saturday as part of the dicastery's 90th anniversary celebrations.
He said: "Today the Pope gives thanks to Eastern Christians for their fidelity at the price of the shedding of blood -- admirable accounts which fill the pages of history even to the present-day martyrology!"
During the visit, the Holy Father publicly announced the appointment of a new prefect for this congregation: Archbishop Leonardo Sandri, who until recently served as undersecretary in the Vatican secretariat of state, overseeing the division of general affairs.
Archbishop Sandri succeeds Cardinal Ignace Moussa I Daoud, 76, who resigned for reasons of age.
Pope Benedict XV, whose pontificate lasted from 1914 to 1922, established the Congregation for Eastern Churches.
Benedict XVI said he took the name of a "Pope who dearly loved the East" because he wants his pontificate to be "a pilgrimage to the heart of the East."
The Holy Father told Eastern Christians that "he wants to stay by their side."
He reiterated "his profound appreciation for the Eastern Catholic Churches for their particular role as living witnesses of the origins."
"Without a continuous connection with the tradition of the origins," the Pope said, "there is no future for Christ's Church."
Esteem and affection
Benedict XVI added: "In a particular way, the Eastern Churches guard the echo of the first announcement of the Gospel; the most ancient memories of the signs performed by the Lord; the first beams of the paschal light, and the reverberations of the unquenchable Pentecost fire.
"Their spiritual legacy, rooted in the teachings of the apostles and the Fathers of the Church, has generated venerable liturgical, theological and disciplinary traditions, showing the ability of 'Christ's thought' to make fruitful cultures and history.
"It is for this reason that I, like my predecessors, feel esteem and affection for the Orthodox Churches: because we are joined by a particularly close bond. We have almost everything in common, and above all, we have in common the sincere hope for unity.
"From the bottom of my heart, I pray that this dream may soon come true."
The Congregation for Eastern Churches supports the Eastern Catholic Churches, helping them to grow, protecting their rights and maintaining in the universal Church the liturgical, spiritual and disciplinary patrimony of the East.
These Churches maintain the traditions and liturgies of the Orthodox Churches, but are set apart by their obedience to the Bishop of Rome.
The Vatican dicastery has authority over the following regions: Egypt and the Sinai Peninsula, Eritrea and northern Ethiopia, south Albania, Bulgaria, Cyprus, Greece, Iran, Iraq, Lebanon, Palestinian territories, Syria, Jordan and Turkey.