North Korea has claimed the right to shoot down US bombers - even if they are not in their airspace
The White House has labeled claims that the US has declared war on North Korea as "absurd."
North Korea has been moving its aircraft and boosting its defences on its east coast, apparently in response to US bombers flying to the Korean peninsula.
The mobilisation came after the US dispatched B-1B jets to South Korea over the weekend, the country's Yonhap news agency reported.
Yonhap claimed it had been told by South Korea's spy agency that the US had released information about the route taken by the B-1Bs because North Korea seemed to be unaware.
North Korea's foreign minister said on Monday that Pyongyang has the right to "shoot down" US planes because Donald Trump had "declared war."
Mr Trump had said that North Korea's leader might not be around much longer - something the North regarded as a "declaration of war."
Ri Yong Ho claimed the country had the right to shoot down the bombers even if they were not in North Korean airspace following President Trump’s tweets.
Mr Ri told reporters in New York: "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."
The Pentagon responded with its own threat, saying that if North Korea did not stop its provocative actions, it would make sure the "President is provided with options to deal with Pyongyang."
However, the White House said that to suggest the US had declared war was "absurd."
"We have not declared war against North Korea and frankly the suggestion of that is absurd," said White House press secretary Sarah Huckabee Sanders.
Mr Ri, who made his remarks before leaving New York following last week's UN General Assembly, added: "In light of the declaration of war by Trump, all options will be on the operations table of the supreme leadership of the DPRK (Democratic People's Republic of Korea)."
"The question of who won't be around much longer will be answered then," he said.
On Saturday, the President tweeted: "Just heard Foreign Minister of North Korea speak at UN. If he echoes thoughts of Little Rocket Man, they won't be around much longer!"
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
Last week, in his first speech to the General Assembly, Mr Trump vowed to "totally destroy" North Korea if it continued to threaten the US and its allies.
The Pentagon called the flight by US bombers a "show of force" designed to demonstrate the range of military options available to President Trump.