Ardern has said she would wait for any findings, after an investigation by the Electoral Commission was immediately referred to the Serious Fraud Office as soon as it was handed to police.
In the latest development last week, NZ First leader Winston Peters claimed photos taken of investigative journalists Guyon Espiner (RNZ) and Matt Shand (Stuff) had been taken by a party supporter - after earlier saying "we took them [the photos]".
Speaking to RNZ's Morning Report today, Ardern kept her distance from the whole affair, saying none of it was a matter for her.
"Indeed, I'm the Prime Minister, I run the government. I do not run three separate parties, so I don't think it's unfair or unreasonable to say that these are matters for New Zealand First, not for me.
"I have a personal view on blogs like that - they're not something that I choose to engage with or have the Labour Party engage with - I don't believe them and think they tend to engage in mudslinging and that's not how I do politics."
She confirmed Peters was safe in his portfolios.
She was asked directly whether - considering the fact he was in her Cabinet and was the deputy Prime Minister and stood in for her when she was unavailable - it was truly not a matter for her.
She was also asked whether Peters' conduct met the threshold required by the Cabinet manual of upholding the highest ethical standards.
"It is not conduct I've been engaged in. No, I don't see these things as being explicit to the Cabinet manual, which is the conduct of how we run the government," she said.
"He maintains the role he needs to maintain appropriately as Minister of Foreign Affairs. You're asking questions of him as leader of a political party ... these are matters for him, I don't even have clarity over who took them (the photos), how they got on a blog post.
"It is ultimately an MMP environment, it will have separate political parties, they are in charge of their own conduct as party and party leaders.
"These aren't matters that I have any responsibility for. I'm the leader of the Labour Party, I had nothing to do with this and I'm not going to stand here and explain it or defend it because it's not for me."
"I cannot run both a government and three political parties."