The statement follows weeks of escalating tensions between North Korea and the United States, fueled by Pyongyang's repeated nuclear tests and Trump's tough talk.
Speaking to Russia's state-run TASS news agency, North Korea's Foreign Minister Ri Yong Ho cited Trump's September speech to the United Nations General Assembly in New York as the tipping point.
"By his bellicose and insane statement in the UN arena, Trump -- it can be said -- lit the wick of the war against us," Ri is quoted as saying on TASS' English language website. "We need to settle the final score, only with a hail of fire, not words."
During his remarks at the UN last month, Trump threatened to "totally destroy" North Korea
and mocked the country's leader, whom he referred to as "Rocket Man."
Ri, who had called Trump "mentally deranged" after the UN speech, told TASS that North Korea was "winning" and represented "a worthy counterweight to the US."
Echoing previous warnings by North Korean leader Kim Jong Un, Ri said, "the United States should act sensibly and stop touching us if they do not want to disgrace themselves in the face of the whole world," adding that his nation's forces "will not leave America, the aggressor state, unpunished."
Ri's comments are likely to continue to fuel a mounting war of words between Trump and Kim.
During an appearance with Canadian Prime Minister Justin Trudeau at the White House on Wednesday, Trump said that while he listens to others around him, he has a "different" attitude when it comes to the North Korea -- one he describes as "tougher."
"I think I have a little bit of a different attitude on North Korea than other people might have. And I listen to everybody, but ultimately, my attitude is the one that matters, isn't it?" Trump said. "That's the way it works. That's the way the system is."
Trump also told reporters that he wants to have the US nuclear arsenal in "tip-top shape,"
pushing back on an NBC report that he wanted to increase the stockpile tenfold.
Asked by a TASS reporter if dialogue between North Korea and the US is possible, Ri said it is not.
"The current situation -- when the US resorts to maximum pressure and sanctions, to outrageous military threats against the DPRK -- is not at all an atmosphere to negotiate," Ri said, according to TASS.