"At the moment we are talking to North Korea through the back door, through the United States. This is dramatic stuff.
"So [it is ] EU first and other countries, but we hope in the long term we've got a free trade deal with North Korea. But not at the moment."
Ardern said Peters' comments were made in the context of the ultimate goal being that countries "play by the rules" and are engaged in the "international world order."
"We have to try to have dialogue with countries like North Korea because that's how we try to de-escalate and denuclearise," she told Newstalk ZB, "And you do that so that they will be part of the international order.
"That was the comment he [Peters] was making. We are not undertaking [an] FTA with North Korea."
Parker said Peters' comments were a "tongue in cheek statement" given that New Zealand had zero trade with North Korea.
"I think he says it almost in jest," Parker told RNZ.
Parker put Peters' comments down to the way he conducts diplomacy.
"Winston Peters is always respectful in the language he uses in respect of other countries and is very slow to insult them," Parker said.
"That's important for a small country like New Zealand and I respect how he does that."