In response, Trump reaffirmed USA involvement in ensuring the security of Japan, pledging that the United States will support its ally Japan 100 percent.
" ... Both agreed to push forward the deployment of THAAD by US forces in Korea", the statement said.
The hardened U.S. stance followed recent North Korean missile launches that Pyongyang described as practice for an attack on United States bases in Japan.
President Trump stated earlier that the US would take action alone to stop North Korea's nuclear program testing if necessary.
Council members "expressed their utmost concern" about North Korea's "highly destabilising behavior and flagrant and provocative defiance of the Security Council".
North Korea test-fired a ballistic missile into the sea off its east coast on Wednesday, South Korea's military said, ahead of a summit between United States and Chinese leaders who are set to discuss Pyongyang's increasingly defiant arms programme.
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North Korea is now building and testing an intercontinental ballistic missile with a solid-fuel motor that could be carried by a small, easily hidden road convoy.
"If we are serious about solving this issue, we need to tackle the root of it", she said at a regular news briefing.
South Korea's foreign ministry strongly condemned the launch, which it said represented a "threat to peace and stability of the whole world".
A spokesman of Moon Jae-in, a presidential candidate of the country's biggest Minjoo Party, criticized the missile launch, saying North Korea's repeated military provocations would only isolate the country and cause pressures and sanctions.
As opposed to the longer distance of 310 miles covered by the KN-15 missile when fired in February, the Wednesday launch covered no more than 40 miles.
The missile launched this week appears to be a new type of missile in the Hyunmoo category, according to the report.
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North Korea fired a ballistic missile into its eastern waters Wednesday, U.S. and South Korean officials said, amid worries the North might conduct banned nuclear or rocket tests ahead of the first summit between President Donald Trump and his Chinese counterpart Xi Jinping this week. Most of North Korea's missiles use liquid propellant, which usually must be added on the launch pad before the weapon is fired.
If confirmed, the test risks raising tensions with China, which protested against South Korea's recent move to allow the U.S.to install an anti-missile system on its territory.
Analysts have said Wednesday's launch of a ballistic missile from North Korea's east coast probably took place with the summit in mind as the reclusive state presses ahead with its missile and nuclear programs in defiance of United Nations resolutions and sanctions.
Photos taken by the club's patrons and later posted on Facebook captured Japanese and US officials responding in real-time to the incident, sparking criticism about why such important meetings were not conducted in a more secure location.
Pyongyang's nuclear weapons program is likely to dominate when Trump meets China's leader on Thursday, their first face to face meeting.
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They have heard North Korean warnings of their destruction for so long that the threats barely even register. President Trump had earlier said China was "working with us" on the issue.