The meeting was chaired by Rex Tilerson, Secretary of State of the United States, which holds the Council's presidency for the month.
"Diplomatic and financial levers of power will be backed up by a willingness to counteract North Korean aggression with military action if necessary".
The United States and South Korea have been holding joint military exercises since early March.
China and Russian Federation both also repeated their opposition to the deployment of a US anti-missile system in South Korea.
Addressing the meeting, Wang said that "we must stay committed to the goal of denuclearization".
U.N. Secretary-General Antonio Guterres says he is alarmed at the risk of military escalation in northeast Asia, "including by miscalculation or misunderstanding", as a result of North Korea's accelerated nuclear and ballistic missile activities.
Denuclearization is the basic precondition for long-term peace and stability on the Peninsula and "what we must accomplish to safeguard the worldwide nuclear non-proliferation regime", he said.
"Nor can other members of this council who are within striking distance of North Korean missiles", he said.
"We urge other partners with direct influence on North Korea to use their leverage to the full, with the aim of easing tensions and ensuring compliance with the expressed will of the United Nations".
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He said, "failing to act now on the most pressing security issue in the world may bring catastrophic consequences".
He says Russian Federation views the developing situation in the region "with alarm" and condemns Pyongyang's nuclear and ballistic missile tests.
The two leaders agreed to reduce tensions in the Korean peninsula through dialogue as they met on the sidelines of a Security Council ministerial meeting.
Ahead of the UNSC session, Chinese Foreign Minister Wang Yi told reporters that a peaceful solution to the Korean crisis is the "only right choice".
Wang warned that "use of force. will only lead to bigger disasters".
"Our past experience of resolving the nuclear issue on the Peninsula shows, whenever dialogue and negotiation were ongoing, the situation on the Peninsula would maintain basic stability and efforts toward denuclearization could make progress", said the minister. For his part, Tillerson expressed gratitude to Wang for attending the ministerial meeting in NY.
"The United States was looking forward to working with China to hold high-level dialogues in various areas, enhance communication, strengthen cooperation and confront challenges", Tillerson said.
He, however, warned that no options are off the table in dealing with the nuclear threat posed by North Korea.