"We know that you don't support animal cruelty and we need your help to prove them wrong! Tell Countdown what you really care about, by encouraging them to make kinder choices that could not only impact the lives of millions of hens - but would be applauded by every caring Kiwi!"
The group encouraged followers to go to Countdown's Facebook page and post a message asking it to "drop all cage eggs".
The message was posted alongside a photo of a hen poking her neck out of a battery cage, with the words: "Countdown don't think you care about her. Show them you do."
Concerned consumers responded as asked, with the supermarket's social media site bombarded with messages.
Briar Douglas said: "Hey Countdown, cage eggs are gross. I would drive really, really far out of my way to shop at a supermarket that only sold free-range animal products."
Bridget Hughes said: "Countdown has the opportunity to be a leader in animal welfare by dropping cage and colony eggs for good."
Melanie Kerr-Brown posted: "Countdown, do the right thing and Ban Caged Eggs."
Sophie Swan said: "Please, Countdown, stop supplying and selling cage eggs. I would go out of my way to stop at Countdown if it became a NZ first in boycotting cage eggs. It's 2016 and time for a positive change in ethical and animal welfare."
In response, Countdown said on Facebook that it had increased its free-range stock, but there was not enough supply to meet demand.
"Over the last few years, our customers have been increasingly moving to Free Range over Caged Eggs and currently around 40 per cent of our egg sales are from non-caged eggs (Free range, Barn & Organic). Almost 30 per cent of those sales are from Free Range eggs," it said.
"At present, there is not enough supply in New Zealand for Countdown to go entirely Free Range and still meet customer demand. This is an issue that affects the whole supermarket industry. However, we are working with suppliers to improve the quantity of Free Range eggs available over time."
As more free-range eggs become available on the market, it said, it was "increasing the proportion of free range eggs in out stores".
"Approximately 60 of our stores already have dedicated more space to Free Range eggs rather than caged eggs.
"We understand there is a steadily growing consumer interest in animal welfare and are committed to satisfying the changing needs of our customers."
However, on its page, Safe said that while it was "great" that Countdown had responded, it was asking "for a phase-out over time, not immediate".
"Please continue to make them aware that caring New Zealanders want them to make a commitment, to name the date, that they will stop selling all cage eggs."