(Adds Republican protest and political criticism)
By Elisabeth O'Leary
MADRID, June 19 (Reuters) - Felipe VI was sworn in as Spain's new king on Thursday and immediately sought to knit together a nation threatened by a growing separatist movement in Catalonia.
In a subdued ceremony, Felipe said there was room in Spain for both unity and diversity, ending a long speech by saying "thank you" in four of Spain's languages: Castilian Spanish, Basque, Catalan and Galician.
Although he holds a largely symbolic role as head of state, supporters hope Felipe will work to keep Spain together and usher in a new era of popularity for the troubled royal household.
Spain is also battling high unemployment, particularly among youngsters who are less monarchist than older generations.
"The monarchy definitely needs a breath of fresh air and I hope Felipe VI brings ideas that will calm those who have their doubts," said Miguel Angel Delgado, 39, an unemployed music teacher who travelled from Seville to join the celebrations.
Felipe, wearing military uniform with a sash and medals, became king after his father, Juan Carlos, abdicated earlier this month following a series of scandals that has led many Spaniards to question the role of the monarchy itself.
"There is room for all of us in a united and diverse Spain," Felipe, 46, said in his speech to dignitaries gathered in the lower house of Parliament. He stressed respect for the diverse cultures and languages within Spain.
The new king waved to well-wishers on the balcony of the royal palace alongside his wife, Queen Letizia, a former journalist, and their daughters, Leonor, age 8, and Sofia, 7, ahead of a reception attended by business leaders, politicians, bullfighters, athletes and comedians.
The royal couple arrived at the palace - a 1738 building used for visits of heads of state and ceremonies - after riding through central Madrid in an open Rolls Royce, escorted by mounted guards with tasseled helmets in a route decorated by red and yellow flowers, the colour of Spain's flag.
Thousands of people lined the route, waving flags and shouting "long live the king" as the mood in the capital turned to celebrations despite reigning soccer champion Spain's crushing World Cup defeat in Brazil on Wednesday.
Security was very tight in central Madrid, with helicopters buzzing overhead and 7,000 police and 120 snipers out on the streets. Spot checks were frequent, and local media reported a handful of arrests for displaying republican flags.
Madrid authorities had denied republicans permission to rally, though protesters clad in the red, yellow and purple flags of Spain's second republic in the 1930s tried to get close to the parade, angering some royal supporters.
Polls show the decision to hand over to Felipe has boosted the popularity of the royals. But two thirds of Spaniards also support the idea of a referendum on whether Spain should continue to be a constitutional monarchy, according to a recent poll by Metroscopia for El Pais newspaper.
"I'm not asking for a republic, but for people to be able to speak out," said 17-year-old student Camilo Buchelli, who joined a short march calling for a referendum. Others chanted "Felipe out."
Local media said three people had been arrested after trying to jump over police barriers. The Interior Ministry could not immediately be reached for comment.
Felipe's multilingual gesture during the ceremony also got a cool response from the regional leaders of Catalonia and Basque Country, who were sitting in Parliament listening to the speech and were notably restrained in their applause.
Leftist parties were sceptical, with Izquierda Abierta (Open Left) calling the speech "empty" and "full of stereotypes" and saying an opportunity had been missed to let people vote on Spain's political system at the polls.
"We have the right to decide, young people want something else," said Julian Rebollo, 73, a retired industrial designer.
The coronation ceremony, at Spain's lower house of parliament, had little pomp and circumstance compared with royal handovers in other countries. It was more of a legal process, attended by lawmakers, high-level politicians and some members of the royal family. No foreign leaders were invited.
The event was designed to chime with times of austerity, palace officials said, mindful that more than one in four Spanish workers is jobless despite an incipient economic recovery.
"We need to win the battle to create jobs, which is Spaniards' primary concern," Felipe said in his speech.
Felipe's father, Juan Carlos, did not attend the event to allow the spotlight to rest fully on the new monarch, according to the palace. His sister Cristina, whose husband is charged with embezzling millions of euros of public funds, and her family were also absent.
Juan Carlos lost favour with crisis-hit Spaniards after going on a secret elephant hunting trip at the height of Spain's financial crisis in 2012. Felipe has distanced himself from his sister, and has remained untouched by the scandals. (Additional reporting by Tracy Rucinski, Raquel Castillo, Tomas Cobos, Fiona Ortiz and Sarah White; Editing by Jeremy Gaunt)