An investigation has been launched into the National Anti-Corruption Commission over its refusal to investigate referrals from the Robodebt Royal Commission.

Attorney-General Mark Dreyfus used fudged data to justify implementing the almost entirely secret National Anti-Corruption Commission, vastly understating the amount of NSW anti-corruption hearings held in public.

Referrals to the Federal Government's new anti-corruption body have exploded more than four-fold in its first two days of operations.