Iceland is currently engaged in accession talks with the EU. However, in fact only a minority of the Members of the Icelandic Parliament, Alþingi, support actual membership. The above picture show the current standings in these matter, based on a) votes in the parliament b) official party programs and c) most recent statements by the MPs in question.
Iceland voted on beginning accession talks two and a half years ago with 33 votes to 28, with 2 abstentions. (There are 63 seats in the Icelandic Parliament). Since then Lilja Mósesdóttir who voted in favor of the talks has withdrawn her support, Þorgerður Katrín who abstained has stated that she wants to finish the talks and two MPs from the movement who voted against the talks, now favor finishing them.
A part of the Left-Green Movement voted to begin the accession talks despite opposing membership as a part of a coalition deal with the Social Democrats (Alliance). Some of them have since reitarated this position. Thus, for the moment there seems to be a majority in the parliament for continuing with the talks (35-28), but not for actually joining the EU.