The tall, 46-year-old former Olympic yachtsman ascends to the throne as his nation struggles with a towering 26-percent jobless rate, smouldering republican sentiment and a growing independence movement in the northeastern region of Catalonia.
"In difficult periods such as these we are going through, past experience in history shows us that only by uniting our desires, putting the common good ahead of individual interests and promoting the initiative, curiosity and creativity of each person, can we manage to advance to better scenarios," Felipe said.
"This is the spirit that everyone — institutional heads, social and economic agents, organisations and citizens — should have so as to decisively confront the future and broaden the field of hope that opens up before us."
The future King Felipe VI, wearing a navy-blue suit, stressed his country's 1,000-year history of unity and diversity as he appeared with his elegant 41-year-old wife Letizia, dressed in a pink jacket, at a cultural award-giving ceremony in northern Spain's Monastery of Leyre.
'Our dear Spain'
It was the royal couple's first joint appearance in public since the 76-year-old Juan Carlos announced on Monday he would abdicate to pass the crown to "a younger generation".
Felipe said he would limit his remarks out of respect for parliament, which has the duty of proclaiming the new monarch in line with the Spanish constitution of 1978.
Yet he promised to devote all his strength to serving the Spanish people and "our dear Spain — a nation, a united and diverse social and political community that has its roots in a millennium-long history".
His comments held special significance at a time when Catalonia's political chief Artur Mas is pushing ahead with plans to hold a vote on independence from Spain on November 9, flying in the face of fierce opposition from Madrid.
A growing number of Catalonia's 7.5 million citizens resent the redistribution of their taxes to other parts of Spain and believe the region would be better off on its own.
At the same time, many Spaniards, especially the young, would prefer to abolish the monarchy.
Thousands of anti-royalist protesters massed in the streets after Juan Carlos' abdication announcement. A group of small leftist parties, too, backed a referendum on the future on the monarchy.
Spain's ruling Popular Party and the main opposition Socialist Party both support the monarchy, however, ensuring Felipe's succession will be approved by parliament, possibly as soon as June 18.
Juan Carlos was widely respected for smoothing Spain's transition to democracy after the death of General Francisco Franco in 1975, in particular for appearing on national television to thwart an attempted military coup in February 1981.
But in a study by pollster Sigma Dos published in January, support for the king, who has been troubled by ill health, gaffes and family scandals, fell to 41 percent.
Those wanting him to abdicate in favour of Felipe surged to 62 percent.
Only 49 percent approved of the monarchy itself.
'No problem with change'
Many Spaniards were outraged to hear the king took a luxury elephant-hunting trip to Botswana in 2012 as they struggled to find jobs in a recession.
This year his youngest daughter Cristina was named as a suspect in connection with her husband Inaki Urdangarin's allegedly corrupt business dealings.
Felipe and Letizia have largely avoided being tainted by the scandals dogging other members of their family, however.
Speaking to reporters during a United Nation event in New York, Spain's Queen Sofia said the changeover to Felipe's reign would be smooth.
"My son represents continuity. There will be no problem with the change," she said.
Asked what advice she could give Letizia, the queen replied: "That she be herself. She is very competent, charming and I love her very much."