Chapter I. Conditions for Authority of Penalties, Sphere of Application of Penal Law et al.
Art. 4
Penalties shall be imposed in accordance with the Icelandic Penal Code on account of the following :-
1. Offences committed within the Icelandic State. If an offence is committed by a person employed on board, or a passenger of, a foreign ship or aircraft travelling here, against a person travelling with that craft or against interests closely linked to the craft, penalty shall, however, only be imposed if the Minister of Justice has ordered investigation and prosecution.
2. Offences committed on board Icelandic ships or Icelandic aircraft, irrespective of a craft's position at the time of commission. If an offence has been committed in a place subject to the criminal jurisdiction of another State under International Law, by a person neither permanently employed on board the craft nor a passenger thereon, penalty shall not be imposed in Iceland unless this is provided for in Articles 5 or 6.
[3. Offences against Art. 264 committed within the Icelandic State, even if the original offence from which the gain has been derived, was committed abroad and irrespective of who caused it]
Jurisdiction
Territorial jurisdiction - national proceedings
EDIT.