Cardinal Laghi was Pope John Paul II's secret emissary to the White House and to several presidents of the United States.

Many in Argentina believe that the church hierarchy supported the generals in their misrule, and that Laghi – who played tennis regularly with one of the leaders of the junta, Admiral Emilio Eduardo Massera – turned a blind eye to the murder and disappearances of thousands.

[citation needed] In his book In the Closet of the Vatican: Power, Homosexuality and Hypocrisy, Frédéric Martel alleges that Laghi was blackmailed by the Argentinean junta into not opposing them because of his use of so-called "taxiboys".

[5] Pope John Paul II transferred him as Apostolic Delegate (10 December 1980) and later (26 March 1984) Pro-Nuncio to the United States.

In that role he helped place conservatives in key positions, such as Bernard Francis Law in Boston and John Joseph O'Connor in New York City.

[6] He made him Cardinal-Deacon of Santa Maria Auxiliatrice in via Tuscolana in the consistory of 28 June 1991, despite the accusations by Argentine writers of links between him and the dictatorship and the "Dirty War" in Argentina.

In 1997 the Dirty War scandal was widely exposed, and, though Laghi denied the charges, it was considered to have ended his chance for the papacy.

On his 80th birthday, 21 May 2002, he became ineligible to vote in a papal conclave but continued to undertake special missions for his friend John Paul II.