Foreign investment may be blocked if it is considered to threaten national security, public order, public safety or public health, or in the event of serious economic, social or environmental difficulties in particular economic sectors or particular areas, which are likely to be of a lasting nature.
"Article 12:
 If the Minister considers that particular foreign investment threatens national security, public order, public safety or public health or in the event of serious economic, social or environmental difficulties in particular economic sectors or particular areas which are likely to be of a lasting nature, he may suspend such an investment, provided that he announces his decision within eight weeks of becoming aware of the investment in question. In the case of investment by a state entity within the European Economic Area, the provisions of Articles 112 and 113 of the Agreement on the European Economic Area shall be observed, cf. Act no. 2/1993. In the case of an investment by a Member State of the European Free Trade Association, the provisions of Articles 40 and 41 shall be observed in the Memorandum of Association.
The Minister may suspend foreign investment in systemically important companies when such investment involves systemic risk.
The Minister is authorized to stop foreign investment according to Art. Paragraphs 2 and 3 on the basis of suggestions from competent authorities.
[Minister] in the first half of each year, the Althingi shall submit a report on foreign investment in business operations in Iceland the year before. It shall include information on the government's measures to increase foreign investment in Iceland, on foreign investment and total investment by industry and on the application of security provisions pursuant to Art. Paragraph 2 and government remedies according to Article 5.[...]" (Act on Investment by Non-residents in Business Enterprises (34/1991), last amended 24 December 2019, Article 12 [google translation])
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"ICELAND
A. Exceptions at national level
I. Investment by established foreign-controlled enterprises
Trans-sectoral: Foreign investment is accepted under reciprocity conditions. Transactions may be blocked if foreign investment is deemed to "seriously reduce competition" or to have an "undesirable effect on the Icelandic Economy". 
Trans-sectoral: Investment by foreign states or state-owned enterprises is prohibited unless an authorisation is granted.[...]" (OECD, National Treatment for Foreign-Controlled Enterprises)
Act on Investment by Non-residents in Business Enterprises (34/1991), last amended 24 December 2019, Article 12
OECD, National Treatment for Foreign-Controlled Enterprises
[<a href="https://www.althingi.is/lagas/nuna/1991034.html">Act</a>],[<a href="https://www.oecd.org/investment/investment-policy/nationaltreatmentinstrument.htm#:~:text=%22National%20Treatment%22%20is%20the%20commitment,domestic%20enterprises%20in%20like%20situations.">NTI</a>]