Trump is overseas on a 12-day Asia-Pacific trip during which he has been meeting with regional leaders with a heavy emphasis on curbing North Korea's nuclear and missile programs.
"Reckless remarks by an old lunatic like Trump will never scare us or stop our advance", the North's Foreign Ministry said in a statement.
As Trump has made his way through South Korea, Japan and China this week - touting the strength of the USA alliance and commanding North Korea to "not try us" - the regime has remained quiet.
"I think we have to be a little patient here for at least a few months to see what more we and others can do, including China", McMaster said.
In a speech to South Korea's Parliament on Wednesday, Mr Trump warned Pyongyang not to underestimate the USA, while offering leader Kim Jong Un a better future if he gives up his nuclear ambitions.
The revelation may have played a part in Trump's extraordinary offer of talks to the North Korean leader.
While North Korea has launched around two dozen missiles this year, including an intercontinental ballistic missile that can strike parts, if not most, of the continental USA, and tested a staged thermonuclear weapon with an explosive yield far greater than anything the regime has previously tested, the North has not engaged in major provocations in almost two months.
Asked if he could see himself being friends with Kim, Trump said: "That might be a unusual thing to happen but it's a possibility".
The US think-tank said: "Although Pyongyang is outspent by its neighbours in dollar-to-dollar comparisons and defence experts say it operates with raging equipment and technology, the regime's forward-deployed military position and missiles aimed at Seoul ensure that Pyongyang's conventional capabilities remain a constant threat to its southern neighbour".
Trump attempted a symbolic stare-down of Kim this week at the heavily fortified border that separates North and South Korea, but heavy fog forced the cancellation of his plans.
Trump, being the man who he is, took the bait and threw some insults back at North Korean leader Kim Jong-un.
He has tried to rally support to curb Pyongyang's rogue weapons programme during his trip, urging regional powers to stand united against North Korea.
At a news conference in Vietnam on Sunday after his tweets, Trump said it was possible he could be friends with Kim one day and that it would be "very, very nice" but he was not sure that it would happen.
He said he asked the Russian leader if he interfered in the 2016 USA election and received assurances from Mr Putin that he "absolutely did not meddle".