At yesterday's election convention, Society member Luka Podrug called Mesic a traitor, after which the president's envoy at the event, Military Chief of Staff General Josip Lucic, walked out. The Society's leadership distanced themselves from Podrug's statement.
Mesic, who is visiting Croatian emigrants in San Francisco, initially declined to comment but later on Saturday did give a statement to the press.
"If the residents of Sinj want the alka to be followed also in another way, then they must also have another standard of behaviour," he said.
"And if they want it to be a small, closed show, then they can have that too," Mesic said, adding, "They can achieve whatever they want".
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.