In 1982 Dąbrowski became titular archbishop pro hac vice and in 1993 senior bishop of the Warsaw Archdiocese.
In December 1981 he wrote a letter to General Wojciech Jaruzelski in which he condemned the proclamation of the martial law in Poland and the subsequent repressions by the regime.
He conducted charitable work on behalf of war-injured children, helping to establish an orphanage home in Izbica Kujawska.
Upon the recommendation of Cardinal Stefan Wyszyński, Pope John XXIII nominated Dąbrowski to the post of auxiliary bishop of Warsaw.
Dąbrowski participated in the crucial Magdalenka and Round Table negotiations which laid the groundwork for the systemic change in Poland (1988 and 1989).