Representatives from the northern Spanish regions of Catalonia, Galicia and the Basque Country issued a joint statement, calling the monarchy "anachronistic".
"The Spanish Monarchy and its figurehead, the king of Spain, do not represent us ... The majority of Catalan, Basque and Galician societies reject the figure of an anachronistic institution", they wrote.
The nationalists accused the monarchy of being rooted in dogmas that survived the dictatorship of Francisco Franco and forcing unity on Spain.
The opening ceremony was attended by Queen Letizia and her two teenage daughters. It came less than a month after the swearing-in of the new left-wing government led by Socialist Prime Minister Pedro Sanchez.