Prime Minister Jacinda Ardern has indicated she would support deputy PM Winston Peters reprising his role as a mediator between the US and North Korea if he is asked.
In a letter delivered by South Korean diplomats yesterday, North Korean leader Kim Jong-un invited Mr Trump to talk, and promised to freeze nuclear and ballistic missile testing while negotiations are underway.
South Korean officials - speaking at the White House - said the North Korean leader was committed to denuclearization.
As special envoy to North Korea a decade ago - appointed by then-US Foreign Secretary Condoleezza Rice - Mr Peters successfully negotiated a deal that delayed the construction of a missile launching pad.
When asked whether she thought Mr Peters could be shoulder-tapped again, Ms Ardern said the government was willing to do whatever was required to facilitate the talks, which are set to happen before the end of May.
"Whatever role we can play we see it as being good for the region, good for the world.
"But it's a matter of us being really available, playing our part as an international actor to encourage talks and dialogue and supporting those sanctions until we see a resolution."
Economic sanctions against North Korea, which New Zealand had supported, had "no doubt" had an influence on that regime's willingness to talk, she said.
Even if there was no immediate outcome from such talks, the fact of them being proposed was "something to be welcomed".
"Open dialogue is something we've wanted to see as opposed to further escalation, and you can't get more high level dialogue than this."
Asked on Newshub Nation today if he thought Mr Trump was the right person to negotiate an agreement, Mr Peters said he would not comment on that.
"If you go back over what has happened over the last nine years since we were last trying to engage with Korea, then this is a potentially decicively different moment. So I'm not going to pour cold water on what looks like potential success."
Mr Peters would not say whether he could have any role in possible talks with North Korea.
Earlier, Mr Peters, who is due to take over as caretaker prime minister for six weeks while Ms Ardern is on maternity leave, said the government welcomed the United States' willingness for talks with North Korea, and North Korea's "reported openness to discuss denuclearisation".
"New Zealand remains firmly committed to denuclearisation of the Korean Peninsula, and we have always encouraged all parties to continue to work toward this goal," he said.
"It has always been our position to advocate for a diplomatic solution. That's why we welcome an indication that these high-level talks may proceed."
Trump-Kim talks show US strategy is working - VP
US Vice-President Mike Pence said North Korea agreeing to discuss denuclearisation "is evidence that President [Donald] Trump's strategy to isolate the Kim regime is working," US Vice-President Mike Pence has said.
He said the US had made "zero concessions" and "consistently increased the pressure" on North Korean leader Kim Jong-un.
It comes only months after the pair hurled insults at each other.
Mr Trump has hailed the dizzying shift in North Korea's position as "great progress" but said sanctions would remain in place.
South Korean envoys earlier briefed the US president on the meeting they had this week with Mr Kim, saying he was now "committed to denuclearisation".
South Korea's President Moon Jae-in said the news of the Kim-Trump meeting had come "like a miracle".
"If President Trump and Chairman Kim meet following an inter-Korean summit, complete denuclearisation of the Korean peninsula will be put on the right track in earnest," he said.
However, correspondents say the North has halted missile and nuclear tests during previous talks, only to resume them when it lost patience or felt it was not getting what it demanded.
In his statement, Mr Pence said the "maximum pressure campaign will continue until North Korea takes concrete, permanent, and verifiable steps to end their nuclear programme".
Mr Trump's strategy has been roundly praised by the South Koreans.
Chinese President Xi Jinping also telephoned him on Friday to welcome the development and urge all sides to show goodwill and avoid doing anything that could impede the improving situation on the Korean peninsula.
The US Secretary of State Rex Tillerson, speaking in Djibouti on an African trip, said of Kim Jong-un: "What changed was his posture in a fairly dramatic way.
"In all honesty, that came as a little bit of a surprise to us, as well that he was so forward-leaning in his conversations with the delegation from South Korea."
- RNZ / BBC