Commenting on the Croatian government's policy towards the tribunal, the society's deputy president, Djuro Perica, said at a news conference in Zagreb that the first person "who dared to reveal a state secret the a source of every evil which has befallen us".
After reporters insisted that he name this person, Perica said that his identity was known, and that he was elected by Croatians twice as their president.
"Unfortunately he is a member of this society," Perica said, adding that he believed "it is high time for Mesic to be expelled from this society".
Perica was supported by the society's president, Marko Veselica, and another vice president, Marko Dizdar, who were also at the news conference.
Perica went on to say that so far nobody had been held accountable for revealing state secrets and documents which in any civilised state would be kept stored in archives for 50 years.
The HDPZ labelled the latest draft proposed by the ICTY Prosecution for an amended indictment against Croatian generals Ivan Cermak and Mladen Markac as monstrous.
The HDPZ leadership criticised both the incumbent and former Croatian governments for what it called a servile relationship with the Hague tribunal's prosecution.
Veselica said that the Hague tribunal had turned into a political instrument of big powers such as Great Britain and the United States.