The general rule is that Foreign Service providers are obligated to pay income tax in Iceland, but can apply for an exemption on the basis of a Double Taxation Convention under certain circumstances.
Foreign Service providers are liable to pay income tax in Iceland but can apply for an exemption on the basis of a Double Taxation Convention. Foreign Service providers that have a permanent establishment in Iceland can not apply for an exemption. The exemption does not include VAT.
The exemption includes salary for posted workers unless they stay in Iceland for more than 183 days in each 12 month period. Included are brief sojourn abroad on account of holidays etc. If the stay exceeds 183 days they have an unlimited tax liability and are liable to pay tax on total income earned in Iceland from arrival.
If a Foreign Service provider that has been exempt from taxation based on a Double Taxation Convention is deemed to have a permanent establishment in Iceland, it is liable to pay income tax on profits attributable to that permanent establishment.
Employees of a service provider that carries on business in Iceland through a permanent establishment are liable to pay tax in Iceland regardless of duration of their stay.
Read more here.
Foreign temporary-work agencies are liable to pay tax in Iceland on payments for services. They can file for exemption from taxation in Iceland regarding payments for their services on the basis of a valid Double taxation convention.
Read more here.
In general, all foreign as well as domestic companies and self-employed business owners selling taxable goods and services in Iceland need to register their business for VAT.
Read more about Value Added tax here. 
Iceland Revenue and Customs