He called immediately for Spain to stay united but respect the cultural differences among its regions, ending a speech by saying "thank you" in several languages: Castilian Spanish, Basque, Catalan and Galician.
Felipe became king after his father Juan Carlos abdicated earlier this month following a series of scandals that led many Spaniards — especially younger generations — to question the role of the monarchy itself.
One of the biggest challenges for Felipe will be whether he can use his symbolic role to spur dialogue between the leaders of Spain and the wealthy north-eastern region of Catalonia, where there is a growing independence movement.
The new king, who is 46, wore military uniform with a sash and swore loyalty to Spain's constitution before addressing dignitaries gathered in the lower house of parliament with a long portion of his speech dedicated to the issue of national unity.
"There is room for all of us in a united and diverse Spain," Felipe said in his speech.
He stressed respect for the diverse cultures and languages within Spain, a clear message to people in Catalonia and Basque Country, who want to break away from Spain
The multilingual gesture, however, got a cool response from the regional leaders of Catalonia and Basque Country, who were sitting in the parliament listening to the speech.