"ISNIC has suspended domains that were used for the website of a known terrorist organisation," the Internet in Iceland Inc authority said in a statement late yesterday.
The site "khilafah.Is" - which ISNIC said was run by a group calling itself Islamic State - was traced back to a web hosting company on the island nation at the weekend and was believed to have been online since mid-September.
Several other websites with the name "khilafah" - or caliphate, an Islamic state which IS militants claim to have established in parts of Iraq and Syria - already exist in other countries with other domain name endings, including ".Com" and ".Org" and without clear links to the group.
In the future, he said, Arabic-language websites using the country's domain would be monitored more closely.
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Some Icelandic media reports suggested that it could prove controversial to close down the site due to Iceland's liberal freedom of speech laws but the domain name authority said in a statement that websites have to be "within the limits of Icelandic law".
"It is impossible that this organisation uses an Icelandic domain and it's very unpleasant that they call themselves IS and use the Icelandic domain," Icelandic Prime Minister Sigmundur David Gunnlaugsson told the daily Morgunbladid.
This has nothing to do with freedom of expression, but criminal and monstrous conduct. We have to be able to shut that down.