In a statement, adopted unanimously, the 15-member council urged the communist nation to show "sincere commitment to denuclearization through concrete action".
The members also "reiterated the importance of maintaining peace and stability" on the Korean Peninsula.
A South Korean government minister has said North Korea's missile program is progressing faster than expected, just hours after the UN Security Council demanded the reclusive country to halt all nuclear and ballistic missile tests.
Speaking Monday in Tokyo, Japanese Chief Cabinet Secretary Yoshihide Suga noted that along with the USA and South Korea, Japan was going to push this week at the United Nations for greater unity, including efforts to extend "diplomatic cooperation with China and Russian Federation and other countries that have a strong influence" over the North.
The council said that launches by North Korea reveal development in nuclear weapons delivery systems, which were increasing tensions around the world.
North Korea on Sunday test-fired a ballistic missile from a region near its west coast amid tense relations with United States, worldwide media reported.
The Security Council is scheduled to hold closed-door consultations on the missile test on Tuesday.
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"The test firing of ICBMs will occur at any time and place, at the will of North Korea's highest leadership", Ji said.
This weekend's successful test could accelerate North Korea's stated goal of developing an intercontinental ballistic missile (ICBM) capable of carrying a small nuclear warhead that could reach the United States.
Speaking at a Chinese economic summit, Put also denied that the test had posed any threat to Russian Federation, despite the weapon landing 60 miles off his nation's east coast.
Aside from space launches, Jeffrey Lewis of the Middlebury Institute of International Studies in the USA said, "this is the longest-range missile North Korea has ever tested".
In April Pyongyang put dozens of missiles on show at a giant military parade through the capital, including one that appeared to be the type launched on Sunday. "But its overwhelming emphasis is diplomatic and economic sanctions".
North Korea warned Washington not to provoke it, saying the "US mainland and Pacific operations" are within range of Pyongyang missiles.
The test was "aimed at verifying the tactical and technological specifications of the newly developed ballistic rocket capable of carrying a large-size heavy nuclear warhead", CNN quoted KCNA as saying.
CBS News correspondent Adriana Diaz reports the missile, described by USA officials as a KN-17 medium range missile, reached an altitude of more than 1,300 miles - fired, North Korea said, intentionally at a high angle out of consideration for its neighbors.
38 North says USA cities aren't at risk today because the full missile system needed to reach them has yet to be tested (this includes re-entry technology needed to return a warhead back into the atmosphere from space).