But the architect of the bill, Green MP Sue Bradford, says the new law is working well and should be left alone.
The first anniversary of the controversial law is tomorrow, a day Unicef says is cause for celebration.
Ms Bradford's legislation amended section 59 of the Crimes Act to remove the defence of reasonable force for parents who physically discipline their children.
The amendment, which was supported by the overwhelming majority of Parliament, gave police discretion to judge whether a reported offence warranted prosecution.
There is to be a review of the law next June, two years after its introduction.
Unicef executive director Dennis McKinlay said fears that good parents would face charges for minor infringements of the law had been well and truly laid to rest.
"Police and the public have shown that this law works well and that parents can find better and more constructive ways to discipline and guide children than hitting them," Mr McKinlay said.
However, Kiwi Party leader Larry Baldock and supporters will on Monday again present signatures on a petition trying to force a referendum that would ask the question: "Should a smack as part of good parental correction be a criminal offence in New Zealand."
When the petition was presented earlier, supporters had collected 324,316 signatures, but after these were checked for validity there were only 269,500 -- less than the 10 percent of enrolled voters which has to be reached for a referendum to be held.
Mr Baldock today said the petition, to be presented to the Clerk of the House on Monday, would be checked and a random sample audited over the next two months to see whether the 285,027 signatures were valid.
Ms Bradford told NZPA today that it was the democratic right of Mr Baldock and his supporters to mount their campaign.
"I think it's a pity that they think it's so important to restore a law which legalises assault of children."
Ms Bradford said she had asked Ministry of Social Development and Child, Youth and Family officials at a select committee on Wednesday whether there had been a noticeable increase in cases or problems because of her bill, "and they said none whatsoever".
"There's still no evidence that I can see of parents being arrested and dragged through the courts for unnecessary reasons or of children being forcibly removed from their parents because they smack, which was all the sort of stuff our opponents put up while the bill was in front of Parliament."
In terms of the broader public perceptions about child discipline, anecdotal and at least one survey had shown more people were realising smacking was the least effective way of disciplining children and were finding other non-violent ways, she said.
"It's going to take a long time for it to fully bed in but I think it's going really well."
