The Local Government Leaders' Climate Change Declaration was introduced to hold regional leaders accountable for taking steps towards reducing carbon emissions.
While the majority of councils have signed it, 23 councils have not yet signed.
The West Coast Regional Council says it hasn't heard enough evidence climate change is real.
Now Thames-Coromandel Mayor Sandra Goudie told The Project she also won't be signing the agreement until it is more fleshed out.
"If you're reading the document more closely, you'll see that we're supposed to be looking after efficiency resources in regards to houses and businesses," she explained.
"We're supposed to be supporting ambitious plans without knowing what those ambitious plans are."
She added that not signing the agreement didn't mean that her council denied climate change.
"We're actually doing quite a lot of stuff to reduce the risk and resilience that people are facing. We really care about our communities, and we're not just sitting on our laurels."
Green Party MP Chloe Swarbrick said in a tweet on Tuesday that the 23 councils that have not signed the agreement is "one reason to care about, engage in, run or campaign for local government."