* Prime minister says bill on EU talks to be tabled

* No timeframe given, one politician expects it next week

* Plenty of support for talks, may be weeks before vote

(Adds details, background)

By Omar Valdimarsson

REYKJAVIK, May 6 (Reuters) - Iceland announced a first step on Wednesday towards potential European Union membership, an unthinkable prospect until the global financial crisis wrecked the island's economy.

Prime Minister Johanna Sigurdardottir said she would present a parliamentary bill authorising the start of membership talks.

Sigurdardottir did not give a timeframe for the tabling of the bill. But one politician, who asked to remain anonymous, told Reuters the government would introduce it next week when parliament convened.

Sigurdardottir's Social Democrats have been in favour of EU talks but their coalition partners, the Left-Greens, have been much more cautious about joining the bloc.