LONDON—Croatia, which next month becomes the newest member of the European Union, wants to join the euro zone as soon as possible despite the problems that have plagued the currency area in recent years, the country's central bank governor said Tuesday.

Croatian National Bank Governor Boris Vujcic said there were few drawbacks to Croatia joining the euro because the country's monetary policy already lacks independence as it is constrained by the high level of euros already used in the country, particularly by banks.

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