Photo: The Canadian Press

North Korea's Foreign Minister Ri Yong Ho at the U.N. Plaza Hotel, in New York, Monday.

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.

Ratcheting up the rhetoric further, the North's top diplomat also argued Monday that Trump's comment gives it the right to shoot down U.S. warplanes in international airspace.

Trump's Saturday tweet said: "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!" 

While the comments may be read as an implicit threat to eliminate Kim, a senior administration official said Washington hadn't changed its policy. 

Military manoeuvres are adding to tensions along the two Koreas' heavily militarized border. In a show of might to North Korea, U.S. bombers and fighter escorts flew Saturday to the farthest point north of the border between North and South Korea by any such American aircraft this century.

North Korea's foreign minister, Ri Yong Ho, said Monday that the world doesn't want "the war of words" between his country and the U.S. to "turn into real action." But he said Trump's claim that "our leadership wouldn't be around much longer" escalates the conflict.

"Given the fact that this comes from someone who is currently holding the seat of (the) United States presidency, this is clearly a declaration of war."

Ri also said North Korea now has "every right" to take countermeasures, including shooting down U.S. strategic bombers "not yet inside the airspace border of our country."