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.
His trip - the first by a United Nations diplomat of his rank since 2010 - saw him meet Foreign Minister Ri Yong-ho and vice-foreign minister Pak Myong-kuk, the North's state news agency KCNA said.
Between Pyongyang's test-firing of a new inter-continental ballistic missile at the end of November (which it says brings the whole of the continental United States within range), and Donald Trump's tit-for-tat threat of completely destroying North Korea, there is a wide gulf of misunderstanding and suspicion that accounts for the hair-trigger tension in the Korean peninsula.
KCNA said North Korean officials and Feltman agreed that his visit helped deepen understanding and that they agreed to communicate regularly.
Feltman stressed the need for relevant Security Council resolutions to be implemented, saying a diplomatic solution could be achieved through honest dialogue. "Time is of the essence", the United Nations said. DPRK is the abbreviation for North Korea's official name, the Democratic People's Republic of Korea.
The launch was the first since September 15, when North Korea fired a ballistic missile over the Japanese island Hokkaido, eventually crashing into the Pacific Ocean.More news: LB in the NFL: JuJu Smith-Schuster Suspended One Game
The move by Seoul, its second set of unilateral sanctions in a month, was created to cut off global sources of funding for North Korea's nuclear missile programme, a foreign ministry official in Seoul said.
North Korean state media earlier said current tensions were "entirely ascribable to the U.S. hostile policy".
The question is "how to convince North Korea that a deal won't be rejected in a year or two by a new American administration", Lavrov said on the sidelines of a meeting of the Organization for Security and Cooperation in Europe. The last time an undersecretary-general for political affairs visited the country was in February 2010.
"We condemned it and demanded that North Korea fully complied with the resolution of the UN Security Council".
The measures are in addition to those imposed by the UN Security Council.
China's foreign minister Wang Yi said Saturday there was still hope for peace on the Korean Peninsula. "He said that all parties need to make efforts to ease the situation and bring the situation out of the "black hole" of confrontation".