Dr. Núñez attended La Salle School in Cuba and graduated as doctor of civil and public law in 1919 from the University of Havana.

He served as a representative and senator from the Las Villas Province and also as the Cuban Minister Plenipotentiary and Envoy Extraordinary to Panama, Peru, Netherlands, Belgium and Luxembourg.

Dr. Núñez Portuondo served as the Cuban Permanent Representative with the rank of ambassador to the United Nations in 1952–1958; and was also Minister of Labor under the interim president Dr. Andrés Domingo y Morales del Castillo in 1954.

Dr. Núñez Portuondo helped József Cardinal Mindzenty of Hungary in assisting refugees into Cuba and the United States.

His eldest son, Emilio Núñez Blanco, elected to the Cuban House of Representatives in 1958, though unable to take office, was the second husband of Mirta Díaz-Balart (the first wife of Fidel Castro).