In May 1973 he and a number of Madrid-based individuals founded the Grupo Tácito, a group of intellectuals, politicians and journalists, some of them coming from the Franco regime and others from the democratic and monarchist opposition to the dictatorship. They - by the prospect of Franco's death - advocated a democratic solution to the dictatorial regime and had influence in different sectors linked to the system, and where active during the period of the Spanish Transition between 1973 and 1976. Oreja came up with the name after the Roman historian Tacitus, meaning that due to government censorship not everything could be said. The Grupo Tácito had its origins in a meeting of the Asociación Católica Nacional de Propagandistas’ (Catholic National Association of Propagandists) and group’s early influence was largely determined by its access to the Catholic press.[1]
Oreja served as Spanish minister of foreign affairs from 5 July 1976 to 1980. July 1976 Oreja set out to reform Spain's 1953 Concordat with the Vatican, which resulted the same month in agreements with the Holy See laying out the separation of church and state.[1] The Spanish chief of state no more had the right to nominate Roman Catholic bishops, in exchange the Vatican dropped its right of "ecclesiastical forum".[2] Two months later Oreja signed the Universal Declaration of Human Rights on behalf of Spain.
At the end of his mandate, Oreja retired from political life, returning to Spain. He continued to be active in many fields, being appointed Head of the Institute for European Studies at the CEU San Pablo University Foundation, Vice-Chair of the BBV Foundation (1996) and Doctor Honoris Causa at Zaragoza and Seville Universities (1996).[7]