He also called Ms Ardern an "utter lightweight" and a "clown" during the show.
Mr Morrison condemned the comment on Thursday, saying it was "way out of line".
Jones partially walked back his words in a statement on Thursday, saying he was "misinterpreted" and that he meant to say "Put a sock in it." But he refused to apologise.
On Friday morning, he returned to the subject, continuing to berate Ms Ardern and reading out messages of support from listeners, including one he claimed was from "a very prominent female political figure" who said, "Alan don't worry, I haven't met a man more supportive of women."
Jones repeated his comments that "Jacinda Ardern has no idea what she's talking about" and called her a "hypocrite" and "gormless", saying: "She has duplicitously excluded agriculture, New Zealand's primary source of greenhouse gas emissions.
"I used the language earlier on and, forgive it, but this is the farting and burping livestock, 50 per cent. So when is Jacinda Ardern going to start culling the dairy herds in New Zealand?"
He then suggested the climate change being faced by Pacific Islanders was a "hoax".
"Even if you accepted that, and you accept that carbon dioxide creates the problem, whatever Australia does or doesn't do at home will make no difference whatsoever to their plight," he said.
Australia is at odds with low-lying Pacific nations, which want a global ban on new coal mines and coal-fired power plants.
The broadcaster previously attracted wide condemnation over his comments about former Australian prime minister Julia Gillard, for which he later apologised. He said she should be "shoved in a chaff bag" and that her father had died "of shame".
Jones is the most listened to Sydney broadcaster in his timeslot.
Nine, the owner of this masthead, owns 54.4 per cent of Macquarie Media, which broadcasts 2GB and 4BC.