"Trump claimed our leadership would not be around much longer," Ri Yong-ho said.
"He(Trump) declared war on our country," the foreign minister said.
On Saturday, US Air Force B-1B Lancer bombers escorted by fighter jets had flown in international airspace over waters east of North Korea for the first time decades.
The Pentagon later said the display of air power demonstrated the range of military options available to President Trump.
President Trump and North Korean leader Kim Jong Un openly traded insults last week with the US President saying North Korea's Foreign Minister Ri Yong Ho and leader Kim Jong Un "won't be around much longer" if Ri echoed the thoughts of "Little Rocket Man", an apparent reference to Kim.
Kim Jong Un enraged at Trump's taunts called the US President "mentally deranged US dotard".