KR's best European success was in 2009–10 UEFA Europa League when they defeated AE Larissa (2–0, 1–1) in the second qualifying round, but were eliminated in next round by Basel (2–2, 1–3). In 2011–12 UEFA Europa League, KR eliminated ÍF Fuglafjørður in the first qualifying round and achieved a big win against MŠK Žilina in the next round (3–0) in Reykjavík and though losing 2–0 in Zilina advanced through to the next round where they lost to Dinamo Tbilisi (1–6 on aggregate).