"The land actually speaks to God. Out of the soil ... Abel's blood spoke to God from a murder. The earth can speak. Leviticus says that the earth convulses under the weight of certain human sin.
"It spews itself up after a while - that's natural disasters. Because nature was never created to carry the bondage of our iniquity," Tamaki said.
"God does not send punishment on people in that kind of a way," reverend Helen Jacobi of Auckland church St Matthew-in-the-City said.
"If that was the case, if you followed that to its logical conclusion, a baby dying of cancer would be somehow sinful, and that's ridiculous. It's just completely illogical."
She said the things people and churches should be, and were focusing on in Kaikoura and other places, was gathering and supporting rather than blaming others for the earthquake.
"They should be helping people get through this terrible time and that's where God is seen in our community - by the way people respond," Jacobi said.
She said evidence of God's presence was not in punishment, but in people doing good to help those in need after Monday's disastrous earthquake.
A Destiny Church spokeswoman said "In view of the terrifying events that have impacted the cities and families of New Zealand over the last few days, our heartfelt condolences go out to the victims affected by the earthquakes and floods over this last week."
She referred the Herald to a blog post by Tamaki, which elaborates further on his Sunday sermon.
In the post, he claims to have warned people of the quake in an "inspired moment" before his sermon began.
Tamaki says that natural disasters are side-effects of environmental pollution, abuse and sexual sins.
Referencing Leviticus, from the Old Testament, he writes: "No other sin in the whole of the bible has any connection to earthquakes, floods and volcanic eruptions, but sexual perversions alone."
In Leviticus, God also warns men not to have sex with varying people including, but not limited to, women with their period, animals, or their sister.