Foreign Minister Ri Yong Ho told reporters that the United Nations and the global community have said in recent days that they didn't want "the war of words" to turn into "real action".
"The whole world should clearly remember it was the United States who first declared war on our country", Ri said. "The whole world should remember USA declared war on our people".
"We have not declared war on North Korea and frankly the suggestion of that is absurd'" said White House press secretary Sarah Huckabee Sanders.
The Trump administration clarified Monday that it's not seeking to overthrow North Korea's government after the president tweeted that Kim Jong Un "won't be around much longer" and Pyongyang interpreted it as a declaration of war.
Regarding who or what country might "last longer", the North Korean official added, "we will see when the time comes".
North Korea has moved its airplanes and strengthened defences on its eastern coast after the U.S. dispatched fighter jets and bombers to the Korean peninsula earlier last weekend, a South Korean intelligence source said on Tuesday.
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But it said a financial crisis kept the country from consistently paying police and military salaries, which presented some risk. President Donald Trump acted "as if he were the world's emperor" at the United Nations last week.
By highlighting the possibility of a potential military clash on the Korean Peninsula, North Korea may be trying to create a distraction as it works behind the scenes to advance its nuclear weapons development, said Du Hyeogn Cha, a visiting scholar at Seoul's Asan Institute for Policy Studies.
While the officials said the exercises are long scheduled and not in response to recent tensions, similar exercises have prompted strong condemnation from North Korea in the past.
"None other than Trump himself is on a suicide mission", Ri told the General Assembly on Saturday. "In case innocent lives of the U.S. are lost because of this suicide attack, Trump will be held totally responsible". Its past nuclear tests have been underground inside North Korea.
American efforts in North Korea aren't aimed at regime change, said the official, who wasn't authorized to comment publicly on the issue and requested anonymity. The North was clearly trying to claim it has the ability to conduct retaliatory strikes against US attacks, said Hong Min, an analyst at Seoul's Korea Institute for National Unification.
In an unprecedented direct statement on Friday, Kim described Trump as a "mentally deranged US dotard" whom he would tame with fire.
Of that flight, Pentagon spokesperson Dana White said, "This is the farthest north of the Demilitarized Zone (DMZ) any US fighter or bomber aircraft have flown off North Korea's coast in the 21st century".