The United States and South Korea conducted large-scale military drills this week, which the North said have made the outbreak of war "an established fact".
After the UN's Under-Secretary-General for Political Affairs Mr Feltman met senior North Koreans all agreed "the current situation was the most tense and risky peace and security issue in the world today", according to the statement.
Our top story this afternoon North Korea and the United Nations have reportedly agreed to hold regular conversations on a variety of issues.
He met North Korean Foreign Minister Ri Yong-ho and visited United Nations project sites amid heightened tensions sparked by the North's Nov 29 test of a new intercontinental ballistic missile that it claims is capable of striking anywhere on the USA mainland.
North Korea's official news agency on Wednesday quoted an unnamed Foreign Ministry spokesman strongly criticizing senior USA administration officials' "bellicose remarks" and the ongoing military exercises.
Dujarric says Feltman told the North Koreans there can only be a diplomatic solution.
"The United Nations expressed concerns over the heightened situation on the Korean peninsula and expressed willingness to work on easing tensions on the Korean peninsula in accordance with the U.N. Charter which is based on global peace and security", KCNA said.
State media also said Feltman visited a Pyongyang maternity hospital and a "disease prevention" facility, but left out mention of details around his meeting with foreign ministry officials.
Trump announced on November 20 that the United States was returning North Korea to the list of state sponsors of terrorism and promised to intensify a campaign of "maximum pressure" and sanctions as part of a rolling effort to compel Kim's government to negotiate over its nuclear program.
Last month's missile test prompted a US warning that North Korea's leadership would be "utterly destroyed" if war were to break out.
It is the first trip of a UN Political Affairs chief to North Korea since his predecessor, also Lynn Pascoe visited in February 2010.