The controversial broadcaster on Thursday criticised Jacinda Ardern after she said "Australia has to answer to the Pacific" on climate change at a forum in the island nation of Tuvalu.

Jones said Ms Ardern was a "joke" for preaching about climate change and said Australian Prime Minister Scott Morrison should "shove a sock down her throat".

Macquarie Media chairman Russell Tate said the comments had caused offence to many people but that Jones has publicly apologised for them.

The breakfast radio host recognised his comments were "careless, unnecessary and wrong" and "should have been more clearly thought out", Mr Tate said.

"He indicated that he had apologised sincerely to Prime Minister Ardern for any offence given, and had certainly not intended to suggest any harm through his comments," the chairman said in a statement on Saturday night.

"Notwithstanding his apologies, I have today discussed the matter with Alan and advised him that any recurrence of commentary of this nature will result in the termination of his contract."

Macquarie Media recently re-signed Jones on a multi-million dollar contract for another two years.

Several advertisers on 2GB, including ME Bank, Snooze and Bing Lee, have indicated they intend to pull advertising from Jones' breakfast following his comments about Ms Ardern.

Ms Ardern herself brushed off the remarks.

"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, meanwhile, said Jones had gone too far.

"I find that very disappointing and of course that's way out of line," he told reporters on Thursday.

It comes less than a week after Nine Entertainment offered to take full ownership of Macquarie, which owns Sydney station 2GB and 3AW in Melbourne.

Australian Associated Press