"I think the comments are not helpful, and in an environment at the moment that is very tense. Everyone wants to avoid military confrontation, and the path ahead there is for North Korea to comply with the UN sanctions and for international pressure to push them in that direction."
New Zealand had not expressed its concern to the US, English said, but would do so if Trump continued to make similar remarks.
Foreign Minister Gerry Brownlee is working with officials on "what to make of the comments and what the implications might be".
"I am worried those comments are not helpful when the situation is so tense, and I think you are seeing reaction from North Korea that indicates that kind of comment is more likely to escalate than to settle things," English said.
Labour foreign affairs spokesman David Parker told the Herald that Trump's language was "as silly as the shock-and-awe language that was used by George Bush before invading Iraq, which has already led to more than a decade of war".
"The most powerful actors in this, other than the United States, are China and Russia. And they, together with the rest of the world, should be increasing the economic pressure on North Korea.
"It is astounding that we have had a President of the United States tweeting about nuclear war, which he has done previously."
Parker said the US was a long-term friend of New Zealand.
"But when they act wrongly - like President Trump is now - they should be left in no doubt as to what New Zealand's opinion is. We should respectfully but clearly communicate that criticism."
On Monday Brownlee issued a press release welcoming a United Nations Security Council Resolution strengthening sanctions on North Korea, after the rogue nation tested intercontinental ballistic missiles on July 4 and 28.
"The unanimous action at the Security Council reflects the international community's grave concern with the ongoing tensions ... it is a strong signal to North Korea to change course," Brownlee said.
