Han Min-koo told South Korea's parliament the test-launch had been detected by the controversial U.S. THAAD anti-missile system, whose deployment in the South has infuriated China.
Russian President Vladimir Putin has told world leaders to stop "intimidating" North Korea following the dictatorship's latest missile test.
USA began talks with North Korean ally China on possible new United Nations sanctions.
SEOUL/GENEVA North Korea's missile programme is progressing faster than expected, South Korea's defence minister said on Tuesday, after the U.N. Security Council condemned the weekend launch of a new long-range missile and demanded Pyongyang halt weapons tests.
It also said that North Korea is "greatly increasing tension in the region and beyond" and that the country should immediately show "sincere commitment to denuclearisation through concrete action".
In a unanimous statement backed by China, the council has promised strong measures in response to Pyongyang's "highly destabilising behaviour" and demanded a halt to "further nuclear and ballistic missiles tests".
The North has staunchly declared that it will not deter its missile and nuclear defense programs even as the United Nations Security Council has repeatedly called for it to do so. Traditionally, the United States and China have negotiated new measures before involving remaining council members.
The White House is calling North Korea a "flagrant menace" after the test launch of a ballistic missile, the seventh such firing this year.
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North Korea fired the missile from the northwestern city of Kusong despite growing threats of increased sanctions from members of the global community.
Sunday's test came less than a week after South Korea elected a new president, Moon Jae-In, who advocates reconciliation with Pyongyang and had expressed a willingness to visit the North to ease tensions.
Experts are viewing the launch as an escalation in Pyongyang's nuclear program, and an indication the North has made major advances in its quest to develop a ballistic missile capable of reaching the US.
Reports say that the missile test was conducted on Sunday, May 14 as supervised by North Korean leader Kim Jong Un.
South Korea's Defense Ministry said more analysis was needed to verify the North's claim on the rocket's technological features. "If the U.S. dares opt for a military provocation against [us] we are ready to counter it". "Clearly, there is a lot more leverage that China has, and we would like China to use", he said.
The Trump administration declared early on that the waiting was over, and followed through by deploying a United States strike group, led by the aircraft carrier the USS Carl Vinson, to the waters off the Korean Peninsula.
The Security Council members expressed their "utmost concern" over the DPRK's "highly destabilising behavior and flagrant and provocative defiance of the Security Council by conducting these ballistic missile launches in violation of its worldwide obligations under United Nations Security Council resolutions", the statement said.
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