A rejection of Icelandic citizenship can be appealed to the Ministry of Justice.

The appeal shall be lodged within three months of the date of notification of the rejection decision. You can send an email to dmr@dmr.is or send a letter to the address of the Ministry of Justice regarding the matter.

You may request the return of original documents and copies of documents that you have submitted to the Directorate of Immigration. You may also request copies of documents related to your case for a fee.

Request for documents | Directorate of Immigration

If you had an application for Icelandic citizenship rejected before, you can apply again later if you are confident that you meet the requirements.