Political involvement

Cardinal Primatesta was considered very influential in the internal workings of the Argentine Church and its relationship to the national government. He was linked to top figures of the military dictatorship of the Proceso; after its downfall in 1983 he defended the stance of the Catholic hierarchy at the time, and opposed institutional self-criticism for it, which the Church only started after Primatesta lost his dominant position. Bishop Emeritus of Morón, Justo Laguna, called Primatesta "a man of little commitment" (un hombre de jugarse poco) and noted that the Cardinal never took a clear position on the issue of Bishop Enrique Angelelli's murder in 1976.

María Elba Martínez, a human rights advocate and lawyer, stated after the Cardinal's death that "Primatesta took a large part of the truth [about the dictatorship] to his grave, mainly about the desaparecidos, the kidnapping of children and the complicity of the ecclesiastic hierarchy with the dictatorship, with the goal of dismembering or weakening the Third World movements of the Second Vatican Council". Martínez further said that Primatesta "was useful" to the military, and that he had "named people" for them.

During the 1990s, Cardinal Primatesta was a strong critic of the neoliberal policies of President Carlos Menem (1989–1999), whom he charged with leaving behind a massive amount of poverty. While in charge of the Social Pastoral Commission he asked for a "social agreement" to overcome the economic crisis of Argentina, and organized discussion meetings for union leaders, businessmen and government representatives. Primatesta mediated also on many social conflicts, including cases where unemployed families took the Cathedral of Córdoba.

On a different note, the Cardinal defended the position of the Church on contraception to the point of denouncing Córdoba Governor Ramón Mestre at the top of his voice for a provincial health program that included handing out condoms near the seat of the Archbishopric.