While such plans may play well among South Koreans exhausted by near-weekly threats from the North and those that fear it may use its weapons as casually as it fires off rhetoric, some analysts say blitzing Pyongyang would bring disaster for South Korea.
A 5.3 magnitude quake had earlier been detected near the test site.
The UN Security Council has condemned the recent missile launches carried out in North Korea, as these violate a resolution made by the 15-nation body.
South Korea's Joint Chiefs of Staff reported that the North launched what appeared to have been a Musudan missile from the northwestern city of Kusong in North Pyongan Province at around 12:33 p.m. Saturday.
The latest test comes ahead of a meeting on Wednesday in Washington of U.S., Japanese and South Korean defense and foreign ministers expected to focus on North Korea's missile and nuclear programs.
Malaysia condemns the test launching of an intermediate-range ballistic missile by the North Korea on Saturday.
Pyongyang said on September 9 that it successfully tested a nuclear warhead that can be mounted on ballistic missiles.
The DPRK is forecast to attempt another launch of a Musudan missile as the latest test failed.
Washington's extended deterrence refers to the stated commitment by the United States to mobilize all military assets, both nuclear and conventional, to defend its allies in crisis.
China's defence ministry said on Monday it was paying close attention to this week's navy drills between the United States and South Korea, and urged them to exercise restraint and not exacerbate regional tensions.
It was seen as a considerable technological advance and the first success by North Korea after several failures.
Defense Minister Han Min-koo leaves for talks with his U.S. counterpart, Defense Secretary Ashton Carter, on Tuesday to attend the 48th Security Consultative Meeting slated for October 19 (Washington time), it said.
Putting the world on notice of another nuclear test would anger the worldwide community, most of which is already considering further sanctions against the reclusive nation for its activity so far.
After the June test, North Korean leader Kim Jong Un boasted that his country had the capability to strike those bases.
Obama has vowed to work with the United Nations to tighten sanctions against North Korea, but has also said that the US was still open to dialogue if the government changes course.
Previously in August, Japanese and South Korean officials said a medium-range ballistic missile flew about 1,000 kilometers (620 miles) and landed near Japan's territorial waters.
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