[6] In February 1956 Múgica, Javier Pradera and Ramón Tamames wrote a manifesto calling to a National University Congress not subjected to the authority of SEU, Falange's student union.

This incident led to the destitution of Education Minister Joaquín Ruiz-Giménez, the decline of SEU which was sidelined from the Youth Front for losing the grip on the student body, and the start of the organized university protest movement.

[10] In 2009 former Catalan President Jordi Pujol claimed in the second volume of his memories that in 1980 Múgica had proposed to him to have Prime Minister Adolfo Suárez replaced by a democratically leaning military.

[12] In 1979 he was a founding executive of the Amistad España–Israel association,[13] and he and his brother Fernando had a leading role in convincing Felipe González to establish diplomatic relations with Israel and managing the process, which was finally sealed in 1986.

[16][17] He harshly opposed the insubordinate movement against the then compulsory military service, admonishing them that the full weight of law would fall on them for "using conscientious objection to destabilize the democratic state and being supported by radicals and violent [elements]".

[18] In September 1990 he was questioned in the Congress of Deputies by Loyola de Palacio for allegedly replying to Cristina Alberdi's petition to increase the female representation in the General Council of the Judiciary as quoted: "Have they installed kitchens in the new offices?".

In 2004, he defended the construction of the Israeli West Bank barrier by the Government of Israel, arguing that it was Palestinian terrorism that "legitimized the fence", which generated great controversy due to the position he held.