Vereitinov qualified for two swimming events at the 2004 Summer Olympics in Athens, by clearing a FINA B-cut of 1:52.55 (200 m freestyle) from the European Championships in Madrid, Spain. In the 200 m freestyle, Vereitinov eclipsed his personal best of 1:51.38 to lead the third heat, but finished only in twenty-seventh place from the morning's preliminaries. He also teamed up with Serhiy Fesenko, Serhiy Advena, and Maksym Kokosha in the 4 × 200 m freestyle relay. Swimming the third leg in heat one, Vereitinov recorded a split of 1:50.34, but the Ukrainians settled for sixth place and twelfth overall, in a final time of 7:24.13.