Jones on Thursday criticised Ms Ardern after she said "Australia has to answer to the Pacific" on climate change during the Pacific Islands Forum in Tuvalu.
The Sydney radio host said Ms Ardern was a "joke" for preaching about climate change, claiming that New Zealand's carbon dioxide had increased per capita more than Australia's since 1990.
He said Australian Prime Minister Scott Morrison should "shove a sock down her throat".
Ms Ardern brushed off the remark when asked what she made of it.
"I don't know that I'm going to give that the light of day, that comment. I think I'll just leave it where it is," she said.
Mr Morrison said Jones had gone too far.
"I find that very disappointing and of course that's way out of line," he told reporters in Tuvalu on Thursday at the Pacific Islands Forum.
"I mean, I have two daughters. So you can expect that's how I would feel personally about it."
Fijian Prime Minister Frank Bainimarama took to Twitter to return serve to Jones, saying it was easy for the broadcaster to make such remarks from the comfort of a radio studio.
"The people of the Pacific, forced to abandon their homes due to climate change, don't have that luxury," he tweeted.
"Try saying that to a Tuvaluan child pleading for help."
"Well said Frank," Mr Turnbull tweeted. "Jones should also apologise to @jacindaardern for his latest misogynistic rant."
New Zealand is emerging as a strong ally with Fiji, with Mr Bainimarama also tweeting about the benefits of having such a friend in tackling climate change.
Mr Jones says he meant to say "put a sock in it".
"This wilful misinterpretation distracts from my point that she was wrong about climate change and wrong about Australia's contribution to carbon dioxide levels," he said in a statement.
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Comments
Firstly it was
Jacinda 1 Trump 0
now its
Jacinda 1 Alan who 0
what an amazing PM we have. Sadly many are jealous of her, particularly middle aged men.
Wherever I travel around the world including Oz, they all say "I wish we had your PM".
Amazing PM? Hopefully, one day NZ will wake up.
things need fixing in new Zealand Where is out PM
I agree Philip that things need fixing in NZ - after 9 years of neglect/. It is being done, be patient.
As for where is our amazing Jacinda -she is doing what John Key did & all other nations leaders are doing and that is attending vital conferences. Geez wouldn't the Philips of this world criticize her is she was the only leader not present!
"Where is out PM".
Likely out fixing stuff.
Is that nine years of neglect or nine years of avoiding groveling to the IMF for more for money, thus greatly increasing our state debt levels? Much money now earned would have gone towards paying interest on the nationwide state debt.
Surely the response of the Australian Prime Minister is also offensive. How does him having two daughters mean he can empathise with our female Prime Minister? What a weird insight. He must relate to our Prime Minister in a fatherly way? That's nice!
out holidaying any fool can see not a lot of fixing .