Prime Minister John Key says he was shocked to learn about David Garrett's passport fraud, which he describes as bizarre behaviour.
The courts have lifted a suppression order covering the case, but the ACT Party's law and order spokesperson is refusing to talk about the incident until Friday.
On Wednesday, Mr Garrett admitted in Parliament that in 1984 he used the identity of a dead infant to get a false passport after reading about the method in the Frederick Forsyth novel The Day of the Jackal.
Mr Garrett told Parliament he admitted obtaining a passport under false pretences but never used it, and in 2005 was discharged without conviction and was granted name suppression.
The admission follows revelations this week that Mr Garrett - who fronted ACT's controversial three strikes legislation - has an assault conviction following an incident outside a bar in Tonga in 2002.
Mr Key says it is up to the public to decide whether Mr Garrett is fit to remain an MP.
He says Mr Garrett's future is a matter for himself and ACT, but the party knew about his past when it selected him as a candidate.
Mr Key says the first he knew about the matter was on Wednesday when it became public.
ACT is one of the Government's support parties. Leader Rodney Hide says Mr Garrett made a terrible mistake, but that does not impair his ability to make a difference as an MP.
Mr Hide is cutting short a trip to Hong Kong to return to New Zealand to deal with the situation. He has already backed Mr Garrett, saying he made a terrible mistake, but has put his past behind him.
Three strikes law defended
Police Minister Judith Collins says she does not believe the involvement of David Garrett in the three-strikes legislation affects its credibility.
Mr Garrett championed the three-strikes law, which means someone convicted of a third serious violence or sexual offence will have to serve the maximum penalty without possibility of parole.
Ms Collins says Mr Garrett's behaviour is a matter for the ACT Party but defended the law, saying it was voted on by Parliament and is a very good piece of legislation.
Govt risks losing credibility, says Goff
Labour Party leader Phil Goff says attempts by Mr Garrett to make excuses for his past behaviour reflect badly on his party and the National Government.
Mr Goff told Morning Report it is hypocritical of Mr Garrett to demand zero-tolerance for crime and criticise name suppression orders.
"I don't think it does any institution any good when a member of that institution preaches one thing, but does exactly the opposite. This is a classic case of do as they say, not do as they do."
Mr Goff says the worst aspect of Mr Garrett's passport fraud was the impact on the family of the dead child.
He says the National Party must put up a credible challenge to ACT Party leader Rodney Hide in the Epsom electorate or damage its own credibility.