Australian radio host Alan Jones has been ordered to make an on-air correction over his "violent metaphors" and inaccurate statements about New Zealand Prime Minister Jacinda Ardern.

The Australian Communications and Media Authority (Acma) found the veteran 2GB broadcaster breached decency rules last year after labelling Ardern a "complete clown".

The other offensive statements included: "I just wonder whether Scott Morrison's going to be fully briefed to shove a sock down her throat", "Now I hope Scott Morrison gets tough here with a few backhanders", and "I hope he goes for the throat this morning."

The Acma found the 79-year-old's statements regarding Ardern "offended against generally accepted community standards of decency".

The broadcaster, who announced his retirement from radio last week citing health issues, attracted more than 125 complaints after the remarks and eventually lost advertisers.

The Acma chair Nerida O'Loughlin said the comments were not appropriate for public radio broadcasting in today's Australia.

"The repeated use of violent metaphors by Mr Jones and his apparent encouragement of aggressive silencing of Ms Ardern was highly offensive and did not meet contemporary community expectations," O'Loughlin said.

"This was evident in the public display of outrage from the community, actions by advertisers and actions by then chairman of Macquarie Media who publicly stated any recurrence of this type of comment would result in the termination of Mr Jones' contract."

Acma also ruled that Jones was in breach of its rules for inaccurate comments on climate change in the same segment.

"These included an incorrect assertion by Jones that biomass is a fossil fuel, and the incorrect presentation of figures relating to Australia's and New Zealand's percentage of energy use from solar and wind. The Acma found that these comparisons were not based on like-for-like data.

Acma decided to take no further action on the decency breaches as Jones had already made an on-air and a written apology and received counselling from management

"Given the imminent retirement of Mr Jones from 2GB and the actions taken by Macquarie Media and Mr Jones at the time, the Acma is not taking further action against the licensee for breach of the decency rules," O'Loughlin said.

2GB will provide an on-air correction over Jones' climate change comments, ACMA says.