Podrug's statement at the Society's election convention in Sinj earlier today prompted Mesic's envoy, Army Chief Of Staff General Josip Lucic, to walk out.
Asked to comment on the incident, President Mesic, who is visiting the United States, briefly told the press in San Francisco, "No comment".
The Alka Society was established in tribute to the people of the Sinj region, southern Croatia, who defeated invading Ottoman Turks in battle in August 1715. In memory of that event, every August the Society organises a jousting tournament in which "alkars", lance-wielding horsemen dressed in traditional costume, match their skills as they target a metal ring ("alka") suspended over a race track.