The two clerics are also expected to sign a joint declaration on church reunification efforts later in the day, as Pope Francis wraps up his three-day visit to Turkey.
On Saturday, the two spiritual leaders attended an ecumenical service in Istanbul at the Patriarchal Church of St. George, which was then followed by private talks between the two.
Earlier in the day, the pope visited other key religious and historical sites: the 17th-century Sultan Ahmet Mosque, also known as the Blue Mosque, and Hagia Sophia, the 6th-century Byzantine church that was transformed into an imperial mosque after the conquest of Constantinople (modern-day Istanbul) and is now a museum.
Additionally, he celebrated Mass at the Catholic Cathedral of the Holy Spirit.
On Friday, the pope was in Turkey’s capital Ankara, where he met with Turkish President Recep Tayyip Erdogan.
During the meeting, Pope Francis urged for respect for religious freedom in the country, particularly its small minority of Christians. According to the BBC, a century ago Christians made up 20% of Turkey's population, but now constitute a mere 0.2% of the predominantly Muslim country. Although Turkey was established as a secular state in 1923, members of the Christian community say they suffer discrimination there, as Islam has reasserted itself in the public sphere. Historically, Christianity played a major role in the area that now constitutes Turkey; the first ecumenical councils, which are connected with the formal establishment of the Christian church in the late Roman Empire, were all held in Turkey.