Uhač was born in
Brseč (Moschiena) in what is now
Croatia. He was educated at the seminary of
Fiume, the seminary of
Venice, the seminary of Gorizia, and the
Pontifical Roman Seminary in
Rome. He also attended the
Pontifical Lateran University in Rome from 1945 to 1954 where he revived a doctorate in theology in 1951 and a doctorate in
canon law in 1954. While at the Pontifical Lateran University he concurrently studied at the
Pontifical Ecclesiastical Academy in Rome where he studied diplomacy. He was
ordained to the priesthood on 16 April 1949 in Rome. After his ordination in Rome he did pastoral ministry in the church of S. Girolamo degli Illirici and further studies, 1949-1954. He joined the Vatican diplomatic service on 1 March 1954. He served as secretary of the nunciature in Panamá. He was created a
Privy chamberlain supernumerary on 25 March 1955. He served as secretary of the nunciature in Egypt, auditor of the nunciature in Germany, of the
nunciature in Spain. He was named counselor of the nunciature in 1967-1970. He was created
Prelate of honour of His Holiness on 16 February 1967. ==Episcopate==