Preliminary results released Friday from a referendum showed 87.6 percent of those who took part wanted changes to a 2007 law which removed the right of parents to use "reasonable force" to discipline their children.
Key said the so-called "anti-smacking law" was working and would remain, but that he would add safeguards to reassure parents they would not be prosecuted for trivial assaults on their children.
"I believe the law is working as intended, but I want to give parents an assurance that a National-led government will continue to monitor the way the law is being implemented," Key said.
No parents have been convicted for light smacking offences against their children since the law was passed two years ago.
"Cabinet has agreed that if future police data indicates a worrying trend, the law will be changed to ensure that good New Zealand parents are not criminalised for lightly smacking," Key said following a cabinet meeting.
Police and other relevant government agencies have been instructed to carry out a review to ensure no parents were being prosecuted for light smacking and there would be regular monitoring of the law.
One of the organisers of the petition calling for the referendum, Larry Baldock, said Key's response was disappointing.
"It sounds like he is basically ignoring the referendum. The things he is offering is not what we asked for, parents don't want to be criminalised for a smack, it's that simple," he told commercial television.
The referendum asked: "Should a smack as part of good parental correction be a criminal offence in New Zealand?"
Voter turnout in the referendum was 54 percent, with just over 1.6 million votes cast, according to the preliminary count.
A 2003 Unicef report said New Zealand had the third-worst rate of abuse and neglect of children in the OECD group of developed countries.