Ri Yong Ho claims his country has the "right to shoot down United States strategic bombers"
North Korea has accused the US of 'declaring war' on its country.
The secretive state has also threatened to 'shoot down' US planes.
Speaking to reporters in New York, North Korean Foreign Minister Ri Yong Ho claimed: "The whole world should clearly remember it was the US who first declared war on our country.
"Since the United States declared war on our country, we will have every right to make countermeasures - including the right to shoot down United States strategic bombers even when they are not inside the airspace border of our country."
White House Press Secretary Sarah Huckabee Sanders responded to Mr Ri's remarks.
She told reporters: “We’ve not declared war on North Korea - frankly, the suggestion of that is absurd.
"It's never appropriate for a country to shoot down another country's aircraft when it's over international waters. Our goal is still the same - we seek the peaceful denuclearisation of the Korean peninsula."
It comes in the wake of escalating tensions between the two countries, with their leaders trading insults and aggressive rhetoric in recent days.
US officials have also taken a number of actions, seen as 'shows of force' against Pyongyang.
On Saturday, the US announced it had flown planes in international airspace over waters east of North Korea.
The Pentagon described it as "a demonstration of US resolve and a clear message that the president has many military options to defeat any threat".
Mr Trump has also signed an executive order to introduce new sanctions against North Korea over its nuclear weapons programme.
In a UN speech last week, the US president described Kim Jong Un as a 'rocket man on a suicide mission'.
He threatened that the US "will have no choice but to totally destroy North Korea" if it has to defend itself or its allies against an attack.
In response, the secretive state's leader - who President Trump later described as a "madman" - said a "deranged" Mr Trump would "pay dearly" for his threat.
Just yesterday, the US leader took to Twitter to declare:
Just heard Foreign Minister of North Korea speak at U.N. If he echoes thoughts of Little Rocket Man, they won't be around much longer!— Donald J. Trump (@realDonaldTrump) September 24, 2017
Pyongyang conducted its sixth and largest nuclear test on September 3rd, and has also threatened to test a hydrogen bomb over the Pacific.
It has also fired two missiles over Japanese territory in recent weeks.