UN High Commissioner for Human Rights Zeid Ra'ad Al Hussein said: "I am very disturbed by the violence in Catalonia on Sunday.
Without that respect there is no living together in peace", continued King Felipe. He did, however, say: "We don't want a traumatic break".
People watching in a bar in Barcelona whistled and booed after the king's speech.
Catalonia, one of Spain's 17 autonomous regions, has some 7.5 million people and includes Barcelona.
He went on to back Spain's government, saying the Catalan referendum for independence was illegal and undemocratic, and adding that the state needs to ensure constitutional order and the rule of law. The turnout was 42.3 percent of the 5.3 million registered voters in the region.