The prime minister says attacking a journalist in the House using parliamentary privilege is "ill-advised".
Mr Jones has faced accusations of a conflict of interest after he attended and spoke at a meeting where a Northland cultural education centre project he had advocated for was discussed.
The project - Manea Footprints of Kupe - was then approved for a $4.6 million grant from the Provincial Growth Fund by Finance Minster Grant Robertson against Treasury advice.
Mr Jones had declared a conflict of interest in the project when he became a minister in November 2017.
Yesterday on Morning Report Mr Jones criticised Stuff journalist Hamish Rutherford who had covered the original story, calling him a "bunny boiler" - a reference from the film Fatal Attraction meaning someone who acts vengefully after being spurned.
Jacinda Ardern told Morning Report it would not be appropriate for Mr Jones to launch an attack on Rutherford.
"Ultimately I have, when asked, said that I did not believe that would be appropriate, and that's my advice to Mr Jones."
She said she spoke to Mr Jones yesterday, and it would be up to him and the Speaker of the House to decide whether his answers to Parliamentary questions on meetings he has attended need correcting.
In an answer to a Parliamentary question in April 2018, Mr Jones said he had had no formal meetings about the project since becoming a minister.
"He knew someone involved in the project and some years ago he'd been told about it and thought it was a good idea and advocated," Ms Ardern said.
"There was no pecuniary interest there, so he has followed the advice Cabinet gave him."
Ms Ardern was asked how Mr Jones' situation was different from former government minister Clare Curran, who was demoted and subsequently quit her ministerial portfolios after failing to disclose separate meetings with then RNZ head of news Carol Hirschfeld and tech entrepreneur Derek Handley.
She said as far as she understood Mr Jones had acknowledged the discussions with Mr Robertson in response to other written questions in Parliament.
Ms Ardern said yesterday she had no intention of sacking Mr Jones, although it would have been better if he had left the room when the project was being discussed.
Mr Jones has previously had to correct 20 answers to questions from the National Party after he failed to disclose meetings he had earlier this year - some of those were with people who have an interest in the Provincial Growth Fund.