The White House has dismissed suggestions that the United States has "declared war" on North Korea as absurd.
"We've not declared war on North Korea. Frankly, the suggestion of that is absurd," White House spokeswoman Sarah Sanders told reporters.
Earlier, North Korea's foreign minister said comments made by US President Donald Trump at the weekend had amounted to a declaration of war on North Korea.
Ri Yong Ho said North Korea reserves the right to take counter-measures, including shooting down US bombers even if they are not in its air space.
Mr Ri said a Twitter message by Mr Trump on Saturday in which the president warned that the minister and North Korean leader Kim Jong Un "won't be around much longer" if they acted on their threats, amounted to a declaration of war.
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
"The whole world should clearly remember it was the US who first declared war on our country," Mr Ri told reporters in New York.
"Since the United States declared war on our country, we will have every right to make counter-measures, including the right to shoot down United States strategic bombers even when they are not inside the airspace border of our country," Mr Ri said.
"The question of who won't be around much longer will be answered then," Mr Ri said.
China's UN Ambassador Liu Jieyi said the escalating rhetoric between the two nations was getting too dangerous and the only solution was negotiations.
"We want things to calm down. It's getting too dangerous and it's in nobody's interest," Mr Liu told Reuters.
"We certainly hope that (the United States and North Korea) will see that there is no other way than negotiations to solve the nuclear issue on the Korean Peninsula... the alternative is a disaster."
On Saturday, US Air Force B-1B Lancer bombers escorted by fighters flew in international airspace over waters east of North Korea in a show of force after a heated exchange of rhetoric between Mr Trump and Mr Kim over North Korea's nuclear and missile programs.
The Pentagon said the flight was the farthest north of the demilitarised zone separating North and South Korea that any US fighter jet or bomber has flown in the 21st century.
"That operation was conducted in international airspace, over international waters, so we have the right to fly, sail and operate where legally permissible around the globe," Pentagon spokesman Colonel Robert Manning said.
North Korea, which has remained technically at war with the US since the 1950-53 Korean War ended in a truce not a peace treaty, has been working to develop nuclear-tipped missiles capable of hitting the US mainland and conducted its sixth and largest nuclear test this month.
North Korea accuses the US, which has 28,500 troops in South Korea, of planning to invade and regularly threatens to destroy it and its Asian allies.
However, the recent spike in rhetoric from both sides has fuelled tensions and raised fears of miscalculation by one side or the other that could have massive repercussions.
The Pentagon said the bomber flight indicated the range of military options available to Mr Trump, but US officials have repeatedly stressed that despite the war or words, the administration prefers a negotiated solution to the crisis.
Colonel Manning responded to Mr Ri's warning about shooting down US bombers by saying it would provide the president with options to deal with North Korea if its provocations continued.
The latest round of heavy verbal salvoes began when Mr Trump threatened in his maiden UN address last Tuesday to "totally destroy" North Korea, a country of 26 million people, if it threatened the US or its allies.
In an unprecedented direct statement on Friday, Mr Kim responded by calling Mr Trump a "mentally deranged US dotard" whom he would tame with fire.
Mr Kim said North Korea would consider the "highest level of hard-line counter-measure in history" against the US and that Mr Trump's comments had confirmed his nuclear programme was "the correct path".
Mr Ri told the UN General Assembly on Saturday that targeting the US mainland with its rockets was inevitable after "Mr Evil President" Trump called Mr Kim a "rocket man" on a suicide mission.
Mr Trump made his controversial response on Twitter following that remark.
