A National MP claims an NZ First MP told him the Government wouldn't fund a project in his electorate unless he kept criticism of the party to himself.

Rodney MP Mark Mitchell claims NZ First MP Jenny Marcroft told him, on behalf of a Minister, to stop attacking NZ First Ministers and advocate for funding from the Provincial Growth Fund.

Ms Marcroft issued an apology to Mr Mitchell on Saturday for "misunderstanding the conversation", and her party leader Winston Peters said she was not under instruction from any NZ First Ministers.

"New Zealand First does not seek to constrain opposition MPs from criticism of the government," Mr Peters said on Monday evening.

"Ms Marcroft apologised to Mr Mitchell for the misunderstanding in their conversation. After the conversation had got out of hand she consulted with me late on Saturday afternoon and was advised by me to issue an apology."

Mr Mitchell made the incident public in a press release on Monday.

"Ms Marcroft said she had been sent to tell me that the Mahurangi River Restoration Project would be considered for funding from the Government's Provincial Growth Fund, but for that to happen I would have to end my involvement with it as a local MP," he said.

"She also said if I ended my involvement and the money was granted, that they did not want National's Regional Economic Development spokesperson Paul Goldsmith asking Shane Jones questions about it in Parliament."

The National MP said Ms Marcroft told him the Government was unhappy with him for his recent criticism of Defence Minister Ron Mark for using a Defence Force aircraft.

"She implied my work as an Opposition MP would be a factor in funding any projects in my electorate I was involved in," he said.

Mr Mitchell said he asked Ms Marcroft to name the colleague who she was speaking on behalf of or he would take the matter further.

"She sent a text message an hour later asking me to forget the conversation," Mr Mitchell said.

The MP said the alleged incident is "rotten behaviour", and called on Ms Ardern to find out which Minister was responsible and "explain what she intends to do about it".

Prime Minister Jacinda Ardern said the process for the fund is "rigorous" and "there is no prerequisite that anyone seeking funding needs to be silent on opposition to the Government".

"I would expect any project regardless of who was advocating for it or who was supporting it to go through that rigorous process," she said.

"There is no prerequisite that anyone seeking funding needs to be silent on opposition to the Government, some of the funding that's already been given has been championed by ex-National MPs or current National MPs.

"That is not the basis on which we grant funding - we grant funding on the basis of a good project that will have clear economic benefits to the local region and local area."

Ms Marcroft has been contacted for comment.

Newshub.