Following education at a Grammar School in Humenné, he applied to study theology at the Comenius University, where he was accepted in 1956 after being turned down three times.

[3] In 1983, following a temporary improvement of the relationship between the Church and the regime, Tkáč was again granted permission to work as a priest and was assigned to the parish in the Červenica village.

As archbishop he opened a new house for priests in Veľký Šariš, renovated the seminary in Košice, established new parishes and presided over the construction of 80 new churches.

[5] In 1997, he defended Jozef Tiso, the fascist president of World War II-era Slovak Republic (1939–1945) and relativized his role in the Holocaust, claiming that "rich and powerful" Jews living overseas did not do enough to save the European Jews.

[6] In 2009 Tkáč reached the age of 75 and, following canonical law, submitted his resignation to Pope Benedict XVI, who accepted it in 2010.