However, the eight-page newsletter distributed in the mail drop claimed the oil had helped to fix people in situations where doctors had been unsuccessful.
"The Holy Oil was chosen by God as an instrument of faith to heal the sick," the newsletter said.
"Learn how to use it to anoint the sick, the emotionally depressed, your loved ones and family, your workplace and objects that represent difficulties or challenges in your life."
A "generous amount of oil", in cross-shaped bottles, would be free to whoever attended the Sunday event at the Vodafone Events Centre in Manukau, the church said. No oil would be sold.
In a series of articles in the newsletter, people claiming to have been healed told their stories. It is not clear what country the stories come from. One church member claimed it helped to cure a pancreatic tumour.
"After anointing herself for a period of time with the oil, [she] went back to the doctors for a check-up. The doctors couldn't find anything! No trace of the tumour was detected," her story read.
Another woman claimed to have had deteriorating eyesight, blood pressure and "pain all over her body". But after attending church and using the olive oil, she said, she was cured.
"At times when I wasn't able to sleep I would anoint myself with oil and I would sleep. Other times, if I felt pain in my stomach, I would use the oil and the pain would disappear.
"If you have faith and use the oil in the name of the Lord Jesus Christ, God will bless you," she said.
Other ailments supposedly cured with the oil were schizophrenia, a heart defect in a three-year-old boy, low iron, skin conditions and bladder problems.
Marriages could also be saved through the use of the oil, the newsletter claimed.
The Herald visited the Universal Church of the Kingdom of God "headquarters" in Otahuhu yesterday. Pastor Renato Fernandes, the congregation head, would not speak about the oil or its supposedly curative powers. He directed inquiries to Bishop Silva.
Bishop Silva would not speak to the Herald, but said in an emailed statement: "Concerning the oil, we don't claim it has healing powers but we believe that faith in God does. Anointing with oil is an act of faith.
"The church does not have specialist medical expertise so people who present themselves at church with an illness are always advised to seek a medical diagnosis from their GP.
"Furthermore, anyone claiming to have been healed whilst attending a [church] service is invariably referred to their doctor because the [church] only recognises healings that have been confirmed by a qualified medical practitioner."
In small print in the newsletter, the church offered the disclaimer: "The UCKG Help Centre does not claim to heal people but believes that God can through the power of faith. Always follow your doctor's instructions."
The deputy chairman of the Medical Association, Stephen Child, said it was an individual's choice if they invested in the olive oil panacea.
While modern medicine had gravitated towards "evidence-based" treatments, nothing could be ruled out in theory, he said.
The "placebo effect" was also proven to be real, Dr Child said, with about 30 per cent of placebo patients in trials getting better.
"We would just hope the patients have the best information available to make a risk-benefit assessment for themselves. If you are willing to take risks ... that's your choice."
The Universal Church of the Kingdom of God has congregations in Otahuhu, Pukekohe and Porirua. It arrived in New Zealand in 2005, having originated in Brazil, where it says it has about 5000 churches.
The church has previously claimed its "divine healing" could help cure HIV, homosexuality, epilepsy and depression.
Bloomberg says the Brazilian founder of the church, Edir Macedo, has become a billionaire from the tithes of his followers.