One member of the public contacted Mayor Dave Cull's office yesterday morning, demanding a public apology from Cr Butcher.
Later in the day, Age Concern Otago chief executive Susan Davidson condemned both comments in a strongly worded email to the Otago Daily Times.
Cr Butcher's choice of words was "ageist", while Cr Thomson's was "also unfortunate", and both needed to do better, Ms Davidson believed.
Cr Butcher first contacted the ODT yesterday morning to reveal the complaint from the member of the public, and to say she was "quite happy" to apologise.
"I apologise if I have upset people - I was referring to myself," she said.
Cr Thomson said the concerns were "a storm in a teacup" and he had no intention of apologising.
"For goodness sake, I can refer to myself however I want ... especially when using it in a relatively lighthearted and self-deprecating manner.
"I don't think an apology is appropriate or warranted."