[citation needed] During and after the Velvet Revolution, from 12 December 1989 to 17 May 1991 (when he resigned) Kováč was the Finance Minister of the Slovak (Socialist) Republic.

He soon became a strong opponent of Prime Minister Vladimír Mečiar and by giving a critical presidential address to parliament in March 1994, Kováč significantly contributed to the deposition of the then Mečiar government and the creation of the Moravčík government (which only lasted until the next parliamentary election in the autumn of 1994).

In 1995 the Mečiar-Kováč conflict intensified and the Movement for a Democratic Slovakia cancelled Kováč's (formal) membership in the party.

The president, opposition parties and Austrian court accused the Slovak intelligence service (SIS) and the government of having organized the kidnapping.

The investigation of new secret intelligence service director Mitro and Slovak police after collapse of Mečiar's regime in the end of 1998 confirmed the participation of the SIS in the abduction, but Slovak courts rejected the trial of its suspected actors because of an amnesty issued by Mečiar on 3 March 1998.