I think Jane's generalization that most European countries require civil marriage before a religious ceremony is valid. This requirement arose largely in territories conquered by Napoleon, which did not, of course, include Sweden. In the U.S., the religious ceremony can suffice for legal validity, presuming that the couple has obtained a marriage license. The requirements vary from state to state.
For while an American priest, minister, or rabbi is authorized by the state to perform marriages, a European cleric is not.
This might come as a surprise for you, but there are many countries in Europe. There is no such thing as a "European cleric". My wife and I got married in a church belonging to the Church of Sweden. The priest was definitely authorized.
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