Trump tweeted over the weekend that North Korean leader Kim Jong Un and his regime "won't be around much longer."
"It is clearly a declaration of war because those were words by an incumbent American president," Ri Yong-ho told reporters in front of his hotel in New York. "As long as the U.S. has declared war, from now on, even if U.S. strategic bombers don't fly into our airspace, we will hold all the rights to self-defense, including the right to shoot them down at a time of our discretion."
He added: "We will see then who lasts longer."
Last week saw an escalation in tensions between Washington and Pyongyang after Trump threatened to "totally destroy" North Korea in the event of an attack on the United States or its allies.
Kim retorted that he would consider the "highest-level" countermeasures, which Ri said could involve the most powerful detonation of a hydrogen bomb over the Pacific Ocean.
On Saturday, the United States flew bombers off North Korea's eastern coast in a show of force.
Soon after, Ri told the U.N. General Assembly a strike on the U.S. mainland was "inevitable" as Trump called Kim "Rocket Man."
"For the past few days, the U.N. and the international community earnestly wished that the North Korea-U.S. war of words would not lead to action," Ri said. "But last weekend, Trump ultimately declared war by saying again that our leadership will not last long."
The U.N. charter recognizes all member states' right to self-defense, he said.