Three men who attempted to enter Australia's Parliament House wearing a Ku Klux Klan hood, a niqab and a motorcycle helmet say they were unfairly treated under new regulations targeting Muslim face veils.

The men want Muslim veils that cover the face banned from the nation's seat of government and said their stunt Monday exposed inequality in the security system that allows visitors to be so dressed.

The three Sydney residents — Sergio Redegalli, Nick Folkes and Victor Waterson — were eventually allowed inside the building, but not with their headwear.

A Department of Parliamentary Services spokeswoman did not immediately provide an explanation for why the men weren't allowed to wear their face coverings inside the building after removing them for identification as the latest rules on face coverings state.