By Ellie Tzortzi

BELGRADE, May 12 (Reuters) - A coalition of pro-Western parties came first in Serbia's parliamentary election on Sunday but faced an immediate challenge from the nationalist runners-up who said they too could form a government.

Independent monitors said the alliance led by the Democratic Party had won 39 percent of the vote, ahead of the nationalist Radical Party which got 29 percent.

The rolling count by the state election commission put the Democrats at 36.7 percent, the Radicals at 28.5 percent.

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

The Democrats celebrated in the streets, and their leader, President Boris Tadic, said: "Serbs have undoubtedly confirmed a clear European path.

"This is a great victory, but it's not over yet," Tadic said. "I want us to be aware that we must form a new government as soon as possible".

The Radicals' leader, Tomislav Nikolic, said the Democrat claim of victory jumped the gun. There were "very clear possibilities of a coalition which does not include the Democratic Party", he said.

Nikolic said he would talk to the two parties that share the Radicals' ideology, the Democratic Party of Serbia led by outgoing nationalist premier Vojislav Kostunica and the Socialists of the late Slobodan Milosevic.

Either these three parties would form a coalition, he predicted, or "Serbia will not have a government at all and we'll have to go to new elections".

EU APPLAUSE

The European Union welcomed the result and urged quick formation of a government with a "clear European agenda".

"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.

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

The EU had made its preference clear before the vote, offering Belgrade a pre-membership pact and a visa facilitation deal that are implicitly conditioned on a Democrat win.

The main pro-EU parties campaigned as one and consolidated their votes in one bloc, slightly increasing their share of the vote in the last general election, in January 2007.

But they still made no great inroads into overall nationalist support, which remained at around 50 percent of the 6.7 million electorate, spread among three parties.

One of the Democrats' choices for a coalition would be a government with the small Liberal Democratic Party -- if it manages to cross the 5 percent threshold needed for seats in parliament -- and minority parties.

An alternative would be an alliance with Milosevic's Socialists, who took 9 percent of the vote. Political sources said that, unlikely as it sounds, it was a favoured option because it would form a stronger coalition.

A coalition with Kostunica, Tadic's ally in the eight-month government that collapsed in March, was seen as unlikely.

Kostunica insists Kosovo is more important than eventual EU membership and has cited "unbridgeable differences" with Tadic over the country's future direction. However, he has yet to respond openly to the Radicals' overtures.

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