Metropolitan Volodymyr, the highest-ranking official of the Moscow-friendly faction of Ukraine's Orthodox Church, made the request in a letter to the Roman Catholic pontiff.
The Ukrainian Greek-Catholic Church practices many eastern rites but is loyal to the pope in Rome. It was banned during Soviet times but has reasserted its influence in western Ukraine since it was made legal again in 1990.
Tensions between the two churches have steadily increased since then, with the Orthodox Church suspecting the Uniate Church of encroaching on its territory and trying to steal its adherents.
The Uniate Church is due to move its seat to Kyiv from the western city of Lviv on 21 August.