Peters is also Foreign Minister and leader of New Zealand First, whose party's donations vehicle - the New Zealand First Foundation - is facing a Serious Fraud Office investigation.
On Monday at her post-Cabinet press conference, Ardern avoided the question when asked if she trusted Peters.
"I have an excellent working relationship with him. We have proven that we can deliver a strong, stable government and ultimately the issue raised today is not a matter for any of us to simply give a word. It is actually for these things to be properly investigated and that is what is happening," she said.
But on Tuesday morning Ardern answered the question directly when asked if she trusted him.
"I do. I work with him every day. I couldn't operate this government without a trusting relationship with Winston Peters, and that is at the core of why we've been able to run that strong, stable government."
Asked why she didn't say that yesterday, Ardern said: "I thought it was implicit in what I said."
She said she did not think the current issues surrounding the NZ First Foundation undermined the integrity of the Government.
"Firstly I'd say that's preempting the outcome. Secondly it's also assuming that those who may be found to be involved are directly involved with the operation of the Government. Neither of those things have been determined yet so let's not get ahead of ourselves."
Ardern said even if the SFO laid charges, Peters' hands might be clean.
"Parties structure themselves differently. Not all party leaders are directly involved with fundraising activity. That's something not for me to clarify, but for those officials in the appropriate place such as the SFO."
She would not be drawn on whether she might stand down Peters if the referral to the SFO led to charges being laid.
"I'm not going to draw judgement until we've seen a conclusion, an outcome, and we don't have that yet here."
Peters had stood aside as Foreign Minister in 2008 when the SFO investigated donations to NZ First made through the Spencer Trust.
Ardern said the SFO would make decisions in its own time.
"They need to be able to do their job without any pressure, without any interference."
But National Party leader Simon Bridges said that voters should know whether charges would be laid against the NZ First Foundation before the election.
Bridges said it was "extraordinary" that Ardern did not directly say if she trusted Peters yesterday.
"This is her Deputy Prime Minister. This is her coalition partner. That is why she is Prime Minister."
Peters has previously said the NZ First Foundation operated in the same way as the National Party Foundation, but Bridges rejected that.
"Any donation to the National Party's foundation is declared and disclosed in relation to electoral laws in exactly the same way as the National Party proper."
He said if a donor gave $10,000 to the foundation and $10,000 to the party, the total would be disclosed as a donation above the $15,000 threshold.
The SFO has laid charges relating to a $100,000 donation to the National Party, but Bridges repeated today that no one in the party had been charged.
"It's entirely disingenuous and misleading to say that somehow the SFO charges in relation to four people are about the National Party."
Bridges said the party was working with the Electoral Commission to return the money at the heart of those charges.
Ardern said electoral finance laws would be reviewed following this year's election and the SFO's work.
"After the conclusion of these investigations, that feels to me the appropriate time to look at our electoral finance laws. I don't think it would be helpful to do that now, mid-stream, when we've obviously still got some lessons potentially to learn."
