Harris, head of the United States Pacific Command, based in Hawaii, said North Korea is "closer to being able to deliver a nuclear-equipped missile anywhere in the world" and called for further coordination between the U.S., Japan and South Korea to deal with the threat.
U.S. Disarmament Ambassador Wood said China was key given that 90 percent of North Korea's trade was with that country.
Addressing reporters after the meeting, the council president, Uruguay's Ambassador Elbio Rosselli, said that "clearly sanctions are a way to go" but stressed support for diplomacy to engage with Pyongyang.
The Security Council "strongly condemned the most recent ballistic missile launches" conducted by Pyongyang on April 28 and May 13, the 15-nation UN body said in a press statement.
The Council has imposed six sets of sanctions against the North since 2006.
Trump warned in an interview with Reuters this month that a "major, major conflict" with North Korea was possible, and in a show of force, sent the Carl Vinson aircraft carrier strike group to Korean waters to conduct drills with South Korea and Japan. "If you are a country that is supplying or supporting North Korea we will call you out on it, we will make sure that everyone knows who you are and we will target sanctions toward you as well".
Haley noted that this weekend's missile came within 60 miles of Russia's border and said Russian Federation is "all wrong".
"We need to return to dialogue with the Democratic People's Republic of Korea, stop intimidating it and find ways to solve these problems peacefully", Putin was quoted as saying, using North Korea's official name.
She said North Korean leader Kim Jong Un is "paranoid" and thinks that the United States is trying to promote regime change and that there are people trying to assassinate him.
"We are willing to talk, but not until we see a total stop of the nuclear process and of any test there", the United States envoy, Nikki Haley, told reporters ahead of a closed-door Security Council meeting.
"We can not be in a "wait and see" mode until the next provocation occurs, " said France's Ambassador François Delattre.
"The conversations that I have had. with my counterpart and in dealing with Beijing is that if (North Korea) did something else and if it looked to be long range, which this does, and if it looks like it is proactively leaning toward an ICBM, which it does, then we would take action", Haley said.