The complainant, Mark Hanna, from the Society for Science Based Healthcare, said there was no evidence that any of those health issues could be alleviated through prayer.
"As such, these claims are in violation of the Therapeutic Products Advertising Code Principle 2, and fail to uphold the high standard of social responsibility required by the Therapeutic Products Advertising Code Principle 3," his complaint read.
The church said it did not provide therapeutic, medical or health services or services which claim a therapeutic purpose.
"We hold prayer meetings, at which the congregation pray about various issues in their lives, including health issues.
"We are no different from any other church in this regard. However we believe that God can heal the sick, and it is He who heals."
The church said it was a combination of people's faith, prayers, the prayers of others, and God's mercy, which did the healing.
The authority's Complaints Board said the church had presented its religious beliefs in evangelical healing as an absolute fact, rather than opinion.
"(It) may mislead and deceive vulnerable people who may be suffering from any of the illnesses listed in the advertisement."
In a majority decision, the board upheld the complaint.
The board had earlier upheld two complaints about the church, including one against an advertisement for olive oil as part of a religious cure-all treatment for everything from tumours and schizophrenia to relationship problems.
Bishop Victor Silva said he had not seen the decision on the prayer sessions, and declined an offer by APNZ to send the decision to him.
He said he would not comment until after he had had a chance to look at the ruling.
The church's website said it was formed in 1977, in Brazil. It established itself in New Zealand in 2005 and was present in more than 95 countries worldwide.
The Complaints Board also upheld two other complaints about companies advertising their products had therapeutic qualities, including amber beads, that claimed to provide relief to teething babies, and detox foot patches, which were said to remove toxins and heavy metals from the user's body.
The Society for Science Based Healthcare said it welcomed the decisions, and hoped the advertisers involved would take the rulings to heart and refrain from making misleading health claims in future.
"These are the latest in a long line of complaints about misinformation regarding healthcare, and as there is still plenty of misinformation out there you can expect to hear more from the society in the future."
The society was a newly formed consumer advocacy group that aimed to "protect consumers' rights to make informed healthcare decisions".
