The laws regarding marriage in Iceland changed on February 1, 2013 and may affect the ability of U.S. citizens to marry in Iceland.  The new law requires that both partners submit a certificate of marital status issued by the relevant authority in their country, state or region.  There is no Federal authority in the United States competent to issue such a statement.  Although the government of Iceland recognizes that some countries do not issue these certificates, they still require a document issued by the relevant authorities in their country, confirming that there are no impediments to the planned marriage.  In the United States, marriage laws are enacted by the governments of the individual states and there is neither a national marriage law, nor a national record of marriages.  Some areas of the United States do recognize that certain foreign countries require such declarations and are able to issue negative records check letters, but not all areas do.  If you are considering getting married in Iceland, check with your local authorities to see if they are able to issue such a declaration.  If you are not able to produce documentation satisfactory to Icelandic authorities you may be denied permission to marry in Iceland.