You need an embassy visa for Turkmenistan if you have an Icelandic passport
Visa options for Turkmenistan
Visitor visa
Travelers need a visa to visit Turkmenistan for Business or Tourism. A paper or embassy visa is the only visa available for travelers visiting Turkmenistan. The visa is typically a stamp or sticker added to the passport. Travelers must obtain this visa from a local embassy, consulate or visa center before traveling.