Citizenship for Children of Icelandic Citizens (1)
Child Born before July 2018
If a child has an Icelandic parent, the child may apply for citizenship or the child's legal guardian may apply on their behalf if the child has not yet reached the age of 18. Various rules apply for eligibility. Note that applications connected to Icelandic citizenship are only available in Icelandic.
Child Born in or after July 2018
A child born to an Icelandic parent in or after July 2018 acquires Icelandic citizenship automatically at birth. If the child is born abroad then Registers Iceland can be notified to register the child, including their citizenship.
Child Born 1964-1982
If a child is born before July 1, 1982 to a mother who is an Icelandic citizen and who is married to the father, who is a foreign citizen, then the child does not automatically acquire Icelandic citizenship at birth. The Icelandic Nationality Act has been amended, however, to include a provision that allows applicants born between July 1, 1964, and June 30, 1982, to declare their right to Icelandic citizenship. Note that applications connected to Icelandic citizenship are only available in Icelandic.
See more at the Directorate of Immigration.