Iceland has closed down a website believed to be used by the jihadist organisation Islamic State and which showed the murder of hostages, the authority responsible for the country's Internet domain name ".is" said Monday.

Internet in Iceland Inc, or ISNIC, made the decision after taking into account "the reputation of the main domain .is", ISNIC head Jens Petur Jensen told AFP.

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.

According to ISNIC, the website's homepage featured the sentence "This is the news publishing website of the Islamic State" in Arabic.

"Among other things, (the website contained) videos that showed executions of the hostages and others," Jensen said.

Several other websites with the name "khilafah" -- or caliphate, which Islamic State 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.

Jensen told Icelandic radio station Bylgjan on Monday that it was the first time the country had to close a website down because of its content.

"We have no experience with this... we have always pointed out that it's none of our business. That the Islamic State had their domain under '.is' was something we feared because of the abbreviation," he said.

Jensen added that the owners of the site did not reply to emails or to phone calls to a British number used for registration. The only physical address for the site was a small roadside shop in New Zealand.

- 'Should we ban hate?' -

In the future, he told public broadcaster RUV, Arabic-language websites using the country's domain would be monitored more closely as websites have to be "within the limits of Icelandic law".

Iceland has been at the forefront of the international debate on Internet freedom, with a strong file-sharing movement and laws prohibiting censorship.

Helgi Hrafn Gunnarsson, a member of parliament from the Pirate Party, which is opposed to Internet censorship, criticised the decision and said people should be able to find out first-hand what the terror group stands for.

"The public has to have the right and opportunity to investigate and discuss openly the ugliest ideas found in human society, especially when we are talking about horror such as the Islamic State," he wrote on Facebook.

Adalheidur Amundadottir, from the Reykjavik-based International Modern Media Institute, which has lobbied to bolster the country's freedom of speech laws, warned that Iceland was in for a difficult debate on Internet censorship.

"We may find the content on this website disgusting, but we nonetheless have to consider if we should ban what we find disgusting, should we ban hate?" she asked in an interview with radio station Bylgian.

Iceland's prime minister, Sigmundur David Gunnlaugsson, ruled out allowing groups like IS to use the country's Internet address, telling the daily Morgunbladid: "I asked the ministry to find out how we can close the site down and prevent it opening again under an Icelandic domain."

"This has nothing to do with freedom of expression, but criminal and monstrous conduct. We have to be able to shut that down."