On 27 July 1997, Sigurvin won his first senior international cap, coming on as a substitute for Sverrir Sverrison in the 1–0 win over the Faroe Islands. It was more than three years until he was selected again for the national team, when he earned his first start for Iceland in the 1–2 friendly defeat to Uruguay on 11 January 2001. He started again two days later in the 3–0 victory against India. He played three more international matches over the following 14 months, all of which ended in defeat for Iceland. Following a spell of more than four years away from the national team, Sigurvin was recalled for the friendly against Spain on 15 August 2006. He made his final Iceland appearance in the goalless draw, coming on as a late replacement for Arnar Viðarsson.
