BRUSSELS, May 5 (Reuters) - The European Union should seek a stronger international role for its euro to avoid being squeezed out of the top world currencies by the rising importance of the Chinese renminbi, the head of the euro zone bailout fund Klaus Regling said.

Regling, who runs the powerful European Stability Mechanism (ESM) fund with a firepower of 500 billion euros, said the EU should work harder on finishing its banking union and capital markets union to boost the euro's standing in the world.

"The economic weight of Europe will continue to shrink in the world because of our demographics, and because emerging markets like China will continue to catch up with the income levels of Europe and the United States," Regling said.

"That means our relative weight will shrink and therefore we should do everything to make our currency more accepted around the world."

The euro was at the moment clearly the world's number two currency, he said, "but if we don't watch out, the Chinese renminbi will become that".

Regling noted that it was the Chinese government's political objective to become less dependent on the dollar.

"There's really the risk that the Chinese renminbi might become the number two in the world, and I think our objective should be to move to a multi-polar currency system with about equal rates for dollar, euro, and renminbi," he said.

"I think that would be good for us and it would be good for the International Monetary system," he told a Belgian central bank seminar. (Reporting by Jan Strupczewski; Editing by Alex Richardson)