(Updates with nationalist challenge)

By Douglas Hamilton

BELGRADE, May 11 (Reuters) - Serbia's pro-European Union president, Boris Tadic, claimed victory over his nationalist rivals in a parliamentary election on Sunday but fell short of a majority and faced an immediate challenge.

The independent monitoring organisation CESID, citing projections of the outcome, said Tadic's Democratic Party and its smaller allies would take 39 percent of the vote.

The Radical Party of hardline nationalist Tomislav Nikolic was running second with 29 percent, it said.

The election was fought on whether Serbs should swallow their anger over EU support for the independence of Kosovo, the Serb province which seceded in February, or turn their backs on the bid for EU membership, Tadic's top priority.

"Serbs have undoubtedly confirmed a clear European path for Serbia," Tadic told supporters at his Democratic Party headquarters. The idea that a nationalist-led government could still take power was unacceptable, he said.

Democratic Party supporters celebrated to fireworks and rock music in the streets outside the party's Belgrade headquarters, but Nikolic quickly disputed the claim of victory.

"There exist very clear possibilities of a coalition which does not include the Democratic Party," he told supporters.

He accused Tadic of a "grave violation of the constitution" by ruling out a coalition of nationalist parties, which collectively were close to a majority of seats.

NO GREAT INROADS

"This election showed that for a majority of Serbs the top objective is a sovereign Serbia within its internationally recognised borders and only secondly European Union membership," Nikolic said.

The Tadic camp picked up votes from smaller parties in a January 2007 election, but made no great inroads into overall nationalist support, which remained at close to 50 percent of the 6.7 million electorate, spread among three parties.

The Radicals have potential allies in the Socialist Party of the late Slobodan Milosevic and the Democratic Party of Serbia led by outgoing nationalist premier Vojislav Kostunica.

It was not yet clear whether the small Liberal Democratic Party had managed to cross the 5 percent threshold needed for seats in the 250-member assembly. If not, Tadic would lose a vital potential ally.

Kostunica, whose support has dwindled, declined to discuss coalitions at a post-election news conference, but spoke of "unbridgeable differences" with Tadic.

CESID put turnout in the watershed election at 60.7 percent.

The European Union welcomed Tadic's projected victory and said it meant Serbia would move ever faster towards membership.

"The pro-European side in Serbia won, which was what we were aiming for in the European Union," Slovenian Foreign Minister Dimitrij Rupel told Reuters in a telephone interview.

"It seems that (President Boris) Tadic's Democrats will have a more important role, which makes me very happy.

"This means that Serbia will move forward ever faster to membership of the EU," said the minister, whose country holds the rotating EU presidency.

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