The Ministry of Justice is not currently doing any work on reviewing name suppression orders, Parliament's Justice select committee says.

In its 2017/18 Annual Review of the Ministry of Justice, the committee says if a court refuses to grant a defendant name suppression, the defendant can apply for the decision to be reviewed within 20 days. If a judge is made aware that a defendant will appeal the decision, interim name suppression will be granted until the appeal is decided.

"Some of us expressed concern that the appeal process may be used to minimise publicity, where there may potentially be no legitimate grounds for an appeal."

The committee says members were also concerned about international news media not complying with name suppression orders.

"A recent example was the case of the murder of Grace Millane, where the accused was named in international media reports, which can be accessed in New Zealand."