On 24 May, 1969, he was appointed Apostolic Delegate to Jerusalem and Palestine, and Titular Archbishop of Mauriana. Laghi received his episcopal consecration on the following 22 June from Amleto Giovanni Cardinal Cicognani, with Archbishop Agostino Casaroli and Bishop Giuseppe Battaglia (who had also ordained Laghi) serving as co-consecrators. During five years in Jerusalem he served as Pro-Nuncio to Cyprus (28 May, 1973) and Apostolic Visitor for Greece. Laghi was then named Nuncio to Argentina on 27 April, 1974.
Pope John Paul II advanced him to Apostolic Delegate (10 December, 1980) and later (26 March, 1984) Pro-Nuncio to the United States, where he was entrusted with emplacing conservatives in key positions, such as Bernard Francis Cardinal Law in Boston and John Joseph Cardinal O'Connor in New York. On 6 April, 1990, John Paul appointed Laghi Pro-Prefect of the Congregation for Catholic Education, and created him Cardinal-Deacon of Santa Maria Auxiliatrice in via Tuscolana in the consistory of 28 June, 1991, despite the exposure by Argentine writers of his links to the past dictatorship and the "Dirty War". On the following 1 July, he was promoted to full Prefect of the congregation.
On 26 December, 1994, the American Time Magazine published an article titled "Who Will Be First Among Us?" which prematurely speculated on who would be the next pope "as John Paul approaches the twilight of his papacy." Laghi was listed among eight cardinals who were considered leading candidates; the article identified Laghi as head of the Congregation for Catholic Education with conservative credentials. 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. He headed the Congregation for Catholic Education until his resignation on 15 November, 1999, and from 1999 to 2001 he was the Cardinal Protodeacon (the longest serving Cardinal Deacon), before exercising his right as a Cardinal Deacon of ten years' standing to become a Cardinal-Priest of San Pietro in Vincoli). 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.
In 2000, Cardinal Laghi was awarded the F. Sadlier Dinger Award in recognition of his outstanding contributions to the ministry of religious education in America.
On 1 March 2003, Cardinal Laghi, as special papal envoy to the United States, met with President George W. Bush and conveyed the Pope's request that the United States reconsider the decision to go to war against Iraq. Bush was photographed with Laghi and commented that he was "an old family friend". During the presidency of Bush's father, George H.W. Bush, Laghi, as Nuncio to the United States, was a frequent guest of the first President Bush and his family.