North Korean state media has recently reported Australia is "showing dangerous moves of zealously joining the frenzied political and military provocations of the US against DPRK".
Brown said Australia was being threatened.
"I think it is very important to note ... that Australia now is in the sights of North Korea. North Korea is saying, hey, because Australia is siding with Great Britain and the United States, by the way, you are in trouble too."
Asked if such comments were an attempt to soften New Zealanders up to gain support in any future conflict or action against North Korea such as a pre-emptive strike, Brown said "absolutely not".
"Kiwis are fiercely independent and they are going to do whatever they are going to do ... your Government has been the first one each and every time to come out and condemn these illegal missile launches ... and threatening to wipe and kill people and blow them out of the world here."
In an interview to be broadcast by CNN on Sunday, former secretary of state and Democratic presidential nominee Hillary Clinton denounces Donald Trump's language towards North Korea, warning it could set off a nuclear arms race in the region.
Prime Minister Bill English has responded to some of Trump's tweets threatening action against North Korea and its leader Kim Jong-un as "unhelpful".
Brown said people either loved or hated Trump's tweets, but such postings were how the President communicated and reached his support base. He said Trump's stance on North Korea was working, with UN sanctions being put in, with boats turned away from North Korea and China playing its part.
"It is emboldening the world to stand up against North Korea and the tyranny and the threats."
Tensions between the US and North Korea have built after Pyongyang tested missiles and a nuclear device.
Brown was asked about other issues, including whether the US would like New Zealand to be more strongly critical of China over the South China Sea dispute. Q&A host Corin Dann noted Australia had been more critical of China.
In response, Brown talked up the closeness of the US-NZ relationship.
"A Five Eyes partner, we had Secretary [Rex] Tillerson come here, you had me...sworn in immediately - Australia doesn't have an Ambassador yet, just for the record...you look at the fact I am working personally with Ambassador [Tim] Groser on the E1 E2 visa issue to stimulate trade."
Brown, a former Massachusetts Republican senator, was one the first ambassadors in the Donald Trump Administration to be confirmed, and arrived in New Zealand in June.