The law on door-to-door sales and distance contracts applies to on-line shopping. This Icelandic law is an implementation of the EU directive on distance selling. It is the Consumer Rights Division of the Consumer Agency that enforces the law on door-to-door sales and distance contracts. However the Agency does not handle individual monetary claims.
In addition other laws can apply to the purchase, for example when buying consumer goods on-line the consumer is also protected by the Sale of Goods and Associated Guarantees Directive 99/44/EC. This directive has been implemented in all EU-states as well as Norway and Iceland.
Please contact your ECC should you have any problems regarding on-line shopping.