In a joint press conference afterwards, they said they were both supportive of US efforts to hold a second summit with North Korean leader Kim Jong Un, which US President Donald Trump said will take place in Hanoi, Vietnam, on February 27 and 28.
"We support complete, irreversible, verifiable denuclearisation on the Korean Peninsula," Payne said.
But they both added that the continued use of sanctions was justified until North Korea could demonstrate denuclearisation.
Peters said verification was critical.
"We should not lighten up our demands for a clear pathway to denuclearisation before we change, for example, our sanctions. We've got to go for broke here in the interests of humanity. And as [Winston] Churchill once said, it's better jaw jaw jaw before war war war."
Speaking to media after the press conference, Peters said he had pushed strongly on the issue of deporting New Zealanders from Australia who had little or no connection with New Zealand.
He cited the case of Wichman Uriaere, who has been ordered to be deported despite having never been to New Zealand.
Uriaere has a New Zealand passport because he was born in the Cook Islands, and is one of more than 1600 New Zealanders ordered to be deported since the beginning of 2015, many of whom have little connection to New Zealand.
Peters said the Australian system was at times "without logical merit" and in some cases "not defensible".
"It comes from the point of view of fairness, really. All we want ... is for there to be some common judicial principles involved, and at this point we've made it clear we do not think that level of judicial propriety is applying at all."
New Zealand has been pleading its case to Australia on this issue for some time, but Peters could not say whether Australia, under new Prime Minister Scott Morrison, would be more receptive.
"I've made a representation and she [Payne] has promised to take it to the highest sectors of Australian political judgement ... I expect it to go the Prime Minister [Morrison]. In the end, that's where the power lies."
Peters said the transtasman relationship was strong, but the countries did not agree all the time.
"It's always disappointing to have a black spot, like people who are being booted out of the country in circumstances that are not, in my view, defensible and we'll just have to keep working on it."
The issue is likely to be revisited when Morrison meets Prime Minister Jacinda Ardern, who has also raised this matter, later this month.
Today's bilateral meeting was also attended by security officials, including director of the NZ Security Intelligence Service Rebecca Kitteridge, head of the Australian Security Intelligence Organisation Duncan Lewis, and Director-General of the Australian Secret Intelligence Service Paul Symon.
Neither Peters nor Payne were prepared to endorse a recent American intelligence report, compiled by US Director of National Intelligence Dan Coats, that accused China of aligning itself with Pacific nations through bribery, investments and diplomatic engagement with local leaders.
Peters said that New Zealand did not hesitate to call out such behaviour, "but I cannot say I'm here to substantiate what he [Coats] said".
Payne agreed, adding that she recently met Coats in the US, but she declined to comment on the substance of their discussion.
Efforts to counter China's influence in the Pacific were apparent last year when Australia announced a $2 billion infrastructure fund for the Pacific, and Australia and the US revealed plans to build a naval base on Manus Island in Papua New Guinea, which had previously been in discussion with China about the project.
Peters also confirmed that he had hosted Payne and the Australian delegation for dinner at his Auckland home last night.
"The purpose was to welcome the Australian delegation over some food and a glass of wine, and have a pretty comprehensive discussion, or walk around the world, so to speak," he said.
Payne also spoke warmly of the transtasman relationship.
"I'm advised the average Australian who visits New Zealand will return three or four times. I've exceeded my quota, so I hope you'll keep inviting me back here."
