* N-VA wins third of vote in Dutch-speaking Flanders
* Support for governing coalition broadly stable
* King to nominate leader of coalition talks (Adds prime minister, N-VA leader, analyst, economist)
By Philip Blenkinsop and Robert-Jan Bartunek
BRUSSELS, May 25 (Reuters) - A party that wants to dissolve Belgium was the chief winner of a parliamentary election on Sunday, setting the scene for months of deadlock before a new government can be formed.
With about 80 percent of votes counted, the opposition N-VA (New Flemish Alliance), had secured a third of the votes from the Dutch-speaking region of Flanders, the economic powerhouse in the north where some 60 percent of Belgians live.
The centre-right party, which captured 28.2 percent of the Dutch-speaking vote in 2010, has proposed transforming Belgium into a loose confederation of linguistically distinct regions, giving more power to regional governments.
It was a sobering night for the socialists of Prime Minister Elio Di Rupo, who lost voters to a newly created hard left party although they should remain the largest force in the French-speaking south of Belgium.
"I hope it will be possible to form a majority which can take our country forward as soon as possible," Di Rupo said.
Belgium's national election comes at the same time that millions across Europe vote for a new European Parliament, with right-wing, anti-EU parties attracting a surge of protest votes in many countries.
However, a day after a gunman shot three people dead at Brussels' Jewish Museum, the far right, anti-immigrant Vlaams Belang (Flemish Interest) was the night's biggest loser.
The electoral system - effectively two elections with separate French-speaking and Dutch-speaking parties appealing to different voters - means at least four parties, and two from each side, will be needed to form a governing coalition.
"The verdict of the Flemish and French-speaking democracies has never been more divided. We don't want a long political crisis, so we also want to take the initiative to see what is possible on the federal level," N-VA leader Bart De Wever told an enthusiastic crowd of supporters in Brussels.
The N-VA is now widely expected to be given a mandate by the king to lead coalition talks though they will be hard pressed to find potential French-speaking allies.
"The N-VA is a big winner and it would be psychologically difficult for the governing parties to just continue with the government without further ado," said Dave Sinardet, politics lecturer at the Free University of Brussels.
However, despite the N-VA's gains, support for the governing parties was broadly stable and they could resume their coalition should its attempts fail.
After the last election in 2010, battles over further devolution and the budget led to 18 months of stalemate before six parties finally agreed to a coalition - an unwanted world record for government formation.
Then, as the would-be partners wrestled over a budget, markets seeking further victims in the euro zone crisis looked to debt-laden Belgium and dumped its bonds, sending the yield on 10-year government paper to almost 6 percent.
Nearly 8 million Belgians voted on Sunday in a far calmer period for the euro zone as a whole and just six days after the AA-rated sovereign sold 10-year debt at a record low of 1.92 percent. (Editing by Alison Williams)