He took over in a formal Mass on 21 July 1972 until he resigned to his Pastoral task on 31 May 1991, upon turning 80 years of age, as established by the Pope. He was succeeded by Rómulo García, becoming then Archbishop Emeritus, where he continued working actively , despite his age.
Mayer spoke both Spanish and German, as well as Italian, among other languages. During the 1980s and 1990s he led many groups of pilgrims from Bahía Blanca to Israel.