The central government has described the referendum as illegal. "Without that respect there is no living together in peace", continued King Felipe.
On Sunday after midnight, Catalan officials claimed that preliminary results of the poll showed 90 percent of the 2.26 million who voted were in favor of independence.
The northeastern province has long considered a vote on independence from Spain.
Some 900 people were injured as police attempted to prevent people casting their ballots in the referendum, which has been controversial in both Spain and Catalonia.
The triumph of "Yes" in the separatist referendum on Sunday in Catalonia, paralyzed by Justice at the request of the Spanish government, has paved the way to a probable unilateral declaration of independence in that autonomous community.
European Council President Donald Tusk said he had spoken to Spain's Prime Minister Mariano Rajoy and had "appealed to find ways to avoid further escalation and use of force".
Al Jazeera's Laurence Lee, reporting from Barcelona, said: "Many people are saying that the mandate, as they see it, of the referendum needs to be accepted and mirrored by the Catalan parliament".
Aleksandar Vucic said Monday his government supports the territorial integrity of Spain, one of five European Union member nations that have not recognized Kosovo.
"We are going to declare independence 48 hours after all the official results are counted", Puigdemont said in the interview.
The vote yesterday saw riot police move in on polling stations in Barcelona and other towns and cities in the Catalan region to stop people from voting, in some cases baton-charging and firing rubber bullets to disperse crowds.
He said: "I honestly think I can join up with the national team because I'm convinced there are thousands of people who totally disagree with what has happened".