SALZBURG, Austria, July 27 (Reuters) - The arrest of Bosnian Serb war crimes suspect Radovan Karadzic showed Belgrade's willingness to recognise its international obligations, and more arrests could follow, the Serbian prime minister said on Sunday.

Karadzic, twice indicted by the U.N. court in The Hague for orchestrating genocide during the 1992-95 Bosnia war, was arrested on Monday after more than a decade on the run.

Serbia's bid to join the European Union had been held up by its failure to comply with demands by the Hague court to hand over Karadzic and other war crimes suspects.

"The arrest of Karadzic was in a way the proof that there is a willingness to cooperate with the (U.N.) tribunal and we believe that cooperation with the tribunal will be essential for our country," Serbian Prime Minister Mirko Cvetkovic told reporters ahead of an annual meeting of the region's prime ministers.

"Karadzic was the number one, so if number one is the proof for the demonstration for willingness, then there is no reason why we wouldn't do that to number two or number seven."

Karadzic's military commander Ratko Mladic and other fugitives are still at large.

Brussels welcomed Karadzic's arrest, saying it was a sign Belgrade was serious about its EU bid, though some states want to see other fugitives wanted for crimes during the Yugoslav wars arrested for Serbia to prove it deserves to join the bloc.

Cvetkovic said Serbia was not expecting a reward for the arrest, though it hoped for improved trading conditions.

"We are doing that because we do believe in international law, but obviously we are expecting that the European Union is giving us this interim agreement to become operational.

The EU signed a long-delayed Stabilisation and Association (SAA) pact with Serbia in April but vowed not to ratify it or unlock its trade benefits until all 27 member states agreed that Belgrade was in full compliance with the U.N. tribunal.

EU Enlargement Commissioner Olli Rehn urged the bloc on Tuesday to grant Serbia improved trading conditions, laid out in the interim agreement -- the trade-related part of the SAA. (Reporting by Karin Strohecker)

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