During World War II and the occupation of Yugoslavia, his family was part of the Nazi-aligned Ustasha movement.

[3] He was decorated with the Order of Ante Starčević for contribution to the maintenance and development of the Croatian statehood idea, establishment and construction of the sovereign Croatian state,[3][4] while he refused to accept 5 decorations which were awarded to him by President Franjo Tuđman.

In 2003, after publishing Steps in History - Memories and Events (Croatian: Koraci u povijesti – sjećanja i događaji), where he criticized Šeks, he was expelled from the party.

[6] In September 2011 he was accused for war crimes by Serbia, along with Vladimir Šeks, Branimir Glavaš, Tomislav Merčep and 40 other Croatian soldiers involved in the Battle of Vukovar.

[8] Vekić was the top candidate on this coalition's list in the 4th electoral district in the 2011 Croatian parliamentary election.