The demand came after it test-fired a new type of tactical guided weapon, its first such test in nearly half a year.
In a statement, Director General of the American Affairs Department at the Foreign Ministry, Kwon Jong Gun accused Mike Pompeo of misrepresenting the meaning of North Korea's requirement for the negotiations.
The statement called for a different counterpart who, it said, is more careful and mature in communicating.
The US has said, it remained ready to negotiate with North Korea. A State Department spokesman said, Washington was aware of Pyongyang's demand but did not comment directly on it.
US Acting Secretary of Defense Patrick Shanahan said the weapons test conducted by North Korea did not involve a ballistic missile.