Han said the Terminal High Altitude Area Defense (THAAD) anti-missile unit deployed by the USA military in the South detected the North Korean missile, marking the first time the controversial system has been put to use since its deployment last month.
North Korea said it was a test of the abilities of a "newly developed ballistic rocket".
North Korean officials claim the recent launch is proof that the nation is capable of delivering a nuclear warhead that could possibly reach the US or its allies.
Some analysts, including officials in Tokyo, estimate that the May 14 launch successfully tested a new type of missile, potentially the longest in North Korea's arsenal.
"To that end, the Security Council demanded the Democratic People's Republic of Korea conduct no further nuclear and ballistic missile tests", the council said, adding that it was ready to impose further sanctions on the country.
The agency said the launch tested its capability to carry a "large-size heavy nuclear warhead".
It also vowed to fully implement the six sanctions resolutions previously adopted and urged all U.N. member nations to implement the measures "in an expeditious and serious manner".
"If South Korea, North Korea, China and Japan have a discussion, I think we have a good possibility of co-hosting the 2030 FIFA World Cup", Chung told reporters.
At the U.N., Francois Delattre, France's ambassador, said Security Council members are preparing to impose new sanctions and strengthen enforcement of existing ones.
The KN-17 missile lifted off near the country's west coast, reaching an altitude of more than 1,300 miles.
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"It appears to have not only demonstrated an intermediate-range ballistic missile (IRBM) that might enable them to reliably strike the US base at Guam, but more importantly, may represent a substantial advance to developing an intercontinental ballistic missile (ICBM)."KCNA said the test launch verified the homing feature of the warhead that allowed it to survive "under the worst re-entry situation" and accurately detonate.The claim, if true, could mark an advancement in the North's ICBM programme exceeding most expectations, said Kim Dong-yub, a professor at Kyungnam University's Institute of Far Eastern Studies in Seoul".
Clustering two to four of the boosters could result in enough power to deliver a 500 kg to one-ton nuclear warhead not only to targets in the west coast of the USA, but even the east coast, some pundits speculate.
The missile travelled some 700km (435 miles), reaching an altitude of 2,000km and landing in the sea west of Japan.
It is not believed that North Korea has the capabilities to make a nuclear warhead that is small enough to mount onto a long-range missile, but some experts do believe that it could arm a missile with a shorter range with a warhead.
On Sunday, North Korea launched a ballistic missile 1,311 miles into the air, exiting the Earth's atmosphere and flying five times higher than the International Space Station, according to the autocratic state's internal media agency.
Kim is testing Moon to determine whether he is going to interact with the USA and China and seek refuge in the alliance as part of a united front against North Korea, or if he is going to reach out to Pyongyang in an effort to seek an inter-Korean solution, Gause said. He has also strongly warned the USA that their rocket has the capability to strike the mainland, reports the Chicago Tribune.
North Koreans cheer after their women's soccer team scored their first goal against South Korea in a qualifying match for the Asian Football Confederation Cup at the Kim Il Sung Stadium in Pyongyang last month.
In Seoul, some citizens expressed frustration.
US President Donald Trump called for tougher sanctions against Pyongyang.
Speaking in China, Putin admitted that the most recent missile test caused his country great concern.