Broadcaster Alan Jones has received death threats on social media following his comments last week about New Zealand Prime Minister Jacinda Ardern.

The 78-year-old breakfast show host had already written and apologised to the Kiwi PM for the comments at the end of last week.

He was said to be "rattled' by the violent nature of the comments directed towards him.

The outrage began after Jones had been firing a trademark tirade at Ms Ardern's "preaching on global warming" at a Pacific Islands Forum in Tuvalu.

"She is a joke, this woman, an absolute and utter lightweight … I just wonder whether Scott Morrison is going to be fully briefed to shove a sock down her throat," he said on his 2GB show.

The comment sparked a social media backlash and Jones had to explain that there had been a "wilful misunderstanding" of his comment.

"Of course what I meant to say that Scott Morrison should tell Ms Ardern to 'put a sock in it'," he said.

When that did not quell the outrage he went further and wrote to the Kiwi PM to apologise.

"Prime Minister, I would like to assure you that I did not intend to suggest any violence towards you," he wrote.

However this morning he received a string of vile and threatening messages on social media. Despite their content he continued on with his breakfast show as normal.