Georgian Byzantine Rite Catholics (Catholics of Georgian nationality or origin who are of Byzantine or "Greek" rite) are not now reported in published sources as existing.
Towards the end of the 19th century, when almost all Georgian Catholics were of the Latin Rite, some wished to use the Byzantine rite used by the Georgian Orthodox Church. The Russian Tsarist government, which had controlled Georgia since the beginning of that century, made use of that rite exclusive to the Eastern Orthodox Church. Accordingly, some of these Georgians, clergy as well as laity, adopted the Armenian Rite and joined the Armenian Catholic diocese of Artvin, which had been set up in Russian Transcaucasia in 1850.
Only after the granting of religious freedom in Russia in 1905 did some Catholics in Georgia adopt the Byzantine rite.
In 1861, outside of Georgia, indeed outside of the whole of the Russian Empire, Father Peter Karishiaranti (Pétre Kharistshirashvili) founded in Constantinople two religious congregations of the Immaculate Conception, one for men, the other for women. These served Georgian Catholics living in the then capital of the Ottoman Empire. They also served in Montauban, France. These congregations are long extinct, although some of their members were still alive in the late 1950s. The building that housed the male congregation, in Feriköy district, still stands in Istanbul, now in private ownership. Their clergy served a small parish in Constantinople, giving Georgian Catholics in the city the possibility to worship in accordance with the Georgian Byzantine rite. This church (Notre-Dame de Lourdes) is still in service, although in the hands of Italian Catholic priests, gravestones in Georgian can still be seen in its courtyard.