Tensions between North Korea and the United States have risen in recent weeks over Pyongyang's nuclear weapons and missile programs.
North Korea has test-fired several missiles and conducted what it said was a test explosion of a hydrogen bomb as it advances toward its goal of developing a nuclear-tipped missile capable of hitting the US mainland.
Speaking to Russia's state-run TASS news agency, North Korean Foreign Minister Ri Yong Ho said his country's nuclear program guaranteed peace and safety in the region and would not be a matter of discussion.
"With his bellicose and insane statement at the United Nations, Trump, you can say, has lit the wick of a war against us," TASS quoted Ri as saying. "We need to settle the final score, only with a hail of fire, not words."
Speaking before the United Nations General Assembly in September, Trump said that the Iranian government is an "economically depleted rogue state" whose chief export is violence and told world leaders the US would "totally destroy" North Korea if necessary,
In his first appearance at the annual gathering of world leaders, the president used a 41-minute speech to take aim also at Iran's nuclear ambitions and regional influence, while addressing North Korea, Venezuela's collapsing democracy and the threat of Islamist extremists.
Ri has previously called Trump "President Evil" and his comments are likely to fuel an escalating war of words between the US President and North Korean leader Kim Jong Un.
"We have almost reached the last point on the journey towards our final goal—to achieve a real balance of power with the United States," he said.