Justice Minister Simon Power wants to see famous people receive the same treatment as everyone else when in court.
Mr Power told the New Zealand Herald a halt should be placed on the emerging "special class" of high-profile people who use their status to attain name suppression.
Read more: Power seeks hard line on court secrecy for celebs
He was responding to a Law Commission report released earlier this week which said well-known people should still be able to argue for suppression if publication would cause "extreme hardship".
Mr Power believes no special rights should be allowed.
"Anybody who makes an application for name suppression should be dealt with on the same grounds, regardless of whether they think they are well known," he said.
"Whether or not somebody believes they are well known, it should not be a ground in itself for name suppression being granted."
The Law Commission's report places onus for the decision to be left to the judge’s discretion.
This month a "prominent entertainer" who forced a teenage girl's face into his genitals was granted permanent suppression to avoid a detrimental effect on his career, including record and ticket sales.
Other cases of "celebrity justice" include the 2005 controversy when an All Black was granted permanent name secrecy despite having pleaded guilty to assaulting his pregnant partner.
Should celebrities be treated like any other criminal in court? Or is that unfair because there is so much more media interest when court cases involve famous people? Have your say below.