"We have called on all nations that have any type of relations, economic activity with North Korea, to join us in putting pressure on the regime in Pyongyang to cause them to rethink the strategy and the pathway they're on with the development of their nuclear weapons program", Tillerson said, according to a transcript provided by the State Department.
"I talked specifically about the withdrawal from the Paris Accord and said New Zealand is concerned about that, and we actually need the United States to play a leadership role in institutions like that, because the issues are too big".
During the trip, Tillerson also said the US believes that "engaging globally remains important".
"The president has been clear to me, "Do not let what's happening over here in the political realm prevent you from the work you need to do in this relationship"," he told reporters in New Zealand.
US Secretary of State Rex Tillerson at Premier House on a bleak Wellington day.
After meeting with the USA top diplomat, New Zealand Prime Minister Bill English said Tillerson had reassured him of the U.S.' ongoing engagement in economic and security spheres in the Asia-Pacific.
"I don't know what the Prime Minister is seeing and hearing from New Zealanders, every New Zealander I talk to expresses concern and sometimes alarm about the conduct of the US President".
'I think we do need to let senior members of the administration know that from our point of view it's not helping worldwide relations and a sense of peace and security around the world, ' he said.
I've never seen so many people flip the bird at an American motorcade as I saw today. "It's served him pretty well and I don't intend to advise him on how to communicate. That's up to him".
Tillerson said he was pleased by reports that some British imams were refusing to offer funeral prayers for the London attackers.
"That is what has to be done", he said.
The secretary of state stressed that "Now, only the Muslim faith can handle this".
Some people who came out in the pouring rain to protest the Trump regime in New Zealand even brought an effigy of the president, complete with his ridiculous "Make America Great Again" hat.
English said he was reassured by Tillerson about the intention of the U.S.to engage in the Asia-Pacific region.