North Korea has moved military aircraft to its east coast and begun boosting defences after claiming the US has declared war.
Pyongyang threatened to to shoot down American bombers flying near the Korean peninsula "even when they are not inside the airspace border of our country".
The warning came after US Air Force B-1B Lancer bombers escorted by fighter jets flew east of North Korea in a show of force following a heated exchange of rhetoric between Donald Trump and Kim Jong-un over Pyongyang's nuclear and missile programmes.
North Korean Foreign Minister Ri Yong-ho claimed the US President's threat that that Kim's regime "won't be around much longer" amounted to a declaration of war and said Pyongyang had the right to take countermeasures.
Tensions have escalated in the region since North Korea conducted its sixth and most powerful nuclear bomb test on September 3 and fired two ballistic missiles over Japan in the past month.
The hostility of the rhetoric reached a new intensity over the last week as the two leaders traded threats and personal insults.
South Korea's Yonhap news agency suggested the reclusive North was bolstering its defences by moving aircraft to its east coast.
The unverified Yonhap report said the US appeared to have disclosed the flight route of its bombers intentionally because North Korea seemed to be unaware.
South Korea's National Intelligence Service was unable to immediately confirm the report.
Mr Ri said on Monday the North's right to countermeasures included shooting down US bombers "even when they are not inside the airspace border of our country".
"The whole world should clearly remember it was the US who first declared war on our country," he told reporters in New York on Monday, where he had been attending the annual United Nations General Assembly.
He added: "The question of who won't be around much longer will be answered then."
White House spokeswoman Sarah Sanders said it was "absurd" to suggest the US had declared war.
The US and South Korea are technically still at war with North Korea after the 1950-53 Korean conflict ended in a truce rather than a peace treaty.
Pyongyang's nuclear test this month prompted a new round of sanctions after the UN Security Council voted unanimously on a resolution condemning the test.
North Korea has been working to develop nuclear-tipped missiles capable of hitting the US mainland, which Mr Trump has said he will not allow.
The North says it needs its weapons programmes to guard against US invasion and regularly threatens to destroy the United States, South Korea and Japan.
But the increasingly personal insults being exchanged between the leaders of the two sides have raised fears a miscalculation could lead to global war.
Mr Trump last week threatened to "totally destroy" North Korea, a country of 26 million people. In response, Mr Kim issued an unprecedented personal statement in which pledged to "tame the mentally deranged US dotard with fire".
White House National Security Adviser H R McMaster defended Mr Trump's rhetoric and said on Monday he agreed Mr Kim might fail to realise the danger he and his country were facing.
However, he also acknowledged the perils of military escalation.
"We don't think there's an easy military solution to this problem," said Mr McMaster, who said he believed any solution would be an international effort.
"There's not a precision strike that solves the problem. There's not a military blockade that can solve the problem," he added.
China, North Korea's sole major ally and largest trading partner, has called for calm and dialogue, while UN Secretary-General Antonio Guterres stressed the only solution to the crisis was a political one.
China's UN Ambassador Liu Jieyi said Beijing wanted the situation "to calm down".
"It's getting too dangerous and it's in nobody's interest," Mr Liu told Reuters in New York.