He said that if the regime of Kim falls, most likely as a result of a United States military strike, either China or the USA should be ready to manage North Korea's nuclear facilities to prevent the spread of the weapons, he said.
Asked about countermeasures, Ri then told reporters in NY that "I think it could be the most powerful detonation of an H-bomb in the Pacific".
"Trump claimed our leadership would not be around much longer", North Korean Foreign Minister Ri Yong-ho told reporters outside his hotel in NY.
This story is breaking and will be updated.
"Since the United States declared war on our country, we will have every right to take counter-measures including the right to shoot down U.S. strategic bombers even when they are not yet inside the airspace border of our country", he said.
Tensions have escalated nearly every day since then.
White House spokeswoman Sarah Sanders on Monday denied the United States had declared war, calling the suggestion "absurd". The U.S. president mocked Kim as a "Rocket Man" on a "suicide mission", and said that the U.S.
On Monday, Ri escalated the threat.
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DPRK refers to the North's official name, the Democratic People's Republic of Korea.
US President Donald Trump and North Korean leader Kim Jong-Un have traded increasingly threatening and personal insults as Pyongyang races towards its goal of developing a nuclear-tipped missile capable of reaching the US. "In case innocent lives of the US are lost because of this suicide attack, Trump will be held totally responsible".
"The question of who won't be around much longer will be answered then", Ri added.
Kim responded to the US President's speech in a rare televised statement in which he said Trump would "pay dearly" for the threats and accused him of being "mentally deranged".
The ongoing war of words between the two nations also saw several new fiery salvos on Saturday, a day on which the United States military, in a show of force, flew bombers in worldwide airspace over waters east of North Korea and the detection of mysterious seismic activity refueled concerns over the rogue nation's nuclear ambitions.
Besides UN sanctions, the USA wants more punitive embargoes on the North for conducting nuclear tests.
Ri, who said North Korea was prepared to test a hydrogen bomb over the Pacific Ocean, told the United Nations on Friday that Trump's disrespect toward Kim made it "inevitable" that rockets would "visit" the USA mainland.
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".