From 1995 to 2010, Björg was a representative of Iceland in various committees under the auspices of the Council of Europe in Strasbourg, particularly in the field of human rights, for example, in the Committee of Experts for the Development of Human Rights (DH-DEV) and the Committee of Experts for the Improvement of Procedures for the Protection of Human Rights (DH-PR) where she served as Chair in 2009 and 2010.