"The aim of the exercise is to practise anti-submarine warfare skills alongside forces from the United States and Japanese self-defence force."
North Korea today said it is "seriously examining" missile strikes on the US territory of Guam. That follows Trump's warning that North Korean threats would "be met with fire and the fury like the world has never seen".
The heated exchange between the countries comes as media reports in the US claim a breakthrough by North Korea means it can now make a nuclear warhead small enough to fit inside its missiles.
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 Foreign Minister Gerry Brownlee issued a press release welcoming a United Nations Security Council Resolution strengthening sanctions on North Korea, after the North tested intercontinental ballistic missiles on July 4 and 28.