"A person would have to do much more than simply post blasphemy to fall foul of the criminal offence in the Harmful Digital Communications Act," Ms Adams said.
The society said the act stated digital communications "should not denigrate an individual by reason of his or her colour, race, ethnic or national origins, religion, gender, sexual orientation, or disability".
Mr Honeychurch said the law would effectively impose some of the world's strictest penalties - including fines of up to $50,000 - on people found guilty of blaspheming, or insulting religion.
"We want to increase social cohesion and understanding, and by awarding privileges and protecting groups from critique we are closing the door on free speech, free inquiry and public debate. New Zealand has to abolish its blasphemy laws before they are used to censor, suppress, and silence public debate," he said.
Mr Honeychurch called the law a "great step backwards from being a progressive society".
The Humanist Society said some human rights organisations took a dim view of the new law for allowing people to bring proceedings if they alleged a digital communication denigrated their religion or caused them to "suffer serious emotional distress".
Last month, lawyers cited in The Law Report said another "possible unintended consequence" of the law would be the establishment of a new legal avenue for recipients of defamatory digital content.
Supporters of the act have said it would address cyber-bullying and the distribution of harmful content online.
The act established a new civil enforcement regime, and new criminal offences to deal with what the Government called "the most serious harmful digital communications".
Ms Adams said it would take a lot for someone to be charged under the act.
"Not only must the perpetrator be responsible for posting the communication, they must intend to harm another person and that harm must actually occur. The offence is targeted at the very worst online behaviours, and will not censor, suppress or silence public debate. Its enactment was recommended by the Law Commission who considered this matter thoroughly."
Ms Adams said that a breach of communication principles does not automatically give rise to civil law remedies under the act.
"So while a communication may 'denigrate an individual by reason of his her colour, race, ethnic or national origins, religion, gender, sexual orientation or disability', it must also be likely to cause serious emotional distress before the approved agency will investigate.
"The test is even higher for someone to apply for district court orders; the applicant must first have been to the approved agency, the breach of the communication principle must be serious or repeated, and the breach must cause or be likely to cause serious emotional distress. Also, the approved agency and the district court will have to act consistently with the Bill of Rights Act and consider the importance of freedom of expression when considering complaints or when the court is making decisions and issuing orders."
Ms Adams said the Human Rights Commission welcomed the new laws to address harmful digital communications and noted that it "aims to strike the right balance between freedom of expression and our need as a community to challenge our bullying culture and protect people who are under attack".
