Storti was a religious Catholic, and in 1948 he left the CGIL to become deputy general secretary of a new Catholic workers' trade union federation. In 1950, this became part of the Italian Confederation of Workers' Trade Unions (CISL), with Storti becoming its assistant general secretary in 1954, and then general secretary in 1958.[1]
The CISL was affiliated to the International Confederation of Free Trade Unions (ICFTU), and in 1959 Storti was elected to its executive committee. In 1965, he became president of the ICFTU, serving until 1972.[1]