Denuclearisation negotiations between Pyongyang and Washington have been deadlocked since a summit in Hanoi broke up in February, and the renewed threats come as a deadline set by Pyongyang for fresh concessions approaches.

Trump on Tuesday indicated that military action was still possible when he was asked about North Korea on the sidelines of a NATO summit in Britain on Tuesday.

"He definitely likes sending rockets up, doesn't he? That's why I call him 'Rocket Man'," Trump said of North Korean leader Kim Jong Un.

"We have the most powerful military we've ever had, and we're by far the most powerful country in the world. And, hopefully, we don't have to use it, but if we do, we'll use it. If we have to, we'll do it," Trump added.

Responding on Wednesday Pak Jong Chon, chief of the General Staff of the Korean People's Army said he was "greatly disappointed" by Trump's comments, the official KCNA news agency said.

He added that "the use of armed forces is not the privilege of the US only".

"If the US uses any armed forces against the DPRK, we will also take prompt corresponding actions at any level," he added, using the initials of North Korea's official name.

North Korea has demanded the US offer it fresh concessions by the end of the year -- ahead of Kim's New Year speech on January 1, a key political set-piece in the isolated country.

Pyongyang has also issued a series of increasingly assertive comments in recent weeks.

Earlier this week, KCNA quoted Vice Foreign Minister Ri Thae Song as saying: "What gift the US receives for Christmas depends entirely on the US' decision."