On Friday, North Korea said the unsafe security situation was due to the "Trump administration's reckless military provocation".
Pence addressed that head-on at the U.S. Army Garrison Yongsan only hours later while speaking to U.S. soldiers as they sat down for their Easter dinner.
President Donald Trump has labeled North Korea a "problem" country that will be dealt with through a broad, and vague, set of options.
The vice president is expected to get several briefings from U.S. officials, including one from Gen. Vincent K. Brooks, head of UN Command in Korea and current commander of USA forces in Korea.
Echoing the remarks of US Secretary of State Rex Tillerson on North Korea last month, Pence said the "era of strategic patience is over".
The North launched a ballistic missile earlier this month ahead of a summit between the United States and China to discuss the North's arms programme.
A South Korean defense official said the action took place in Sinpo, a port city in eastern North Korea.
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According to ABC News, a Defense Department official said that a ballistic missile launch "blew up nearly immediately". The high-profile failure came as the North tried to showcase its nuclear and missile capabilities around the birth anniversary of the North's late founder and as a USA aircraft carrier neared the Korean Peninsula.
North Korean nuclear tests were previously followed by angry condemnations and threats of more sanctions.
Earlier in the week, following his meeting with Chinese President Xi Jinping, Trump said the US would take unspecified action against North Korea if Beijing doesn't cooperate.
McMaster's use of "provocative" and "destabilizing" to describe North Korea echoes administrations of both parties that have attempted to rally others on the global stage, including China, to help prevent fresh war on the peninsula.
Mr Pence flew to South Korea on the first stop of a four-nation Asia tour meant to show America's allies - and remind its adversaries - that the Trump administration is not turning its back on the increasingly volatile region.
National security adviser Lt. Gen. H.R. McMaster said Sunday "all our options are on the table, undergoing refinement and further development" in reaction to the North Korean nuclear program.
President Donald Trump is asserting that China is working with the United States on "the North Korea problem".
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Yang and Tillerson also discussed the implementation of those agreements reached by the two countries' presidents, during their first meeting in the US state of Florida earlier this month, reports Xinhua.
The tests and resultant harsh warnings appear to have put the United States and North Korea - two nuclear powers - on a collision course. The administration's immediate emphasis, the officials said, will be on increasing pressure on Pyongyang with the help of Beijing.
Early assessments were that the launch was not of the intercontinental ballistic missile that North Korea has reportedly been trying to develop.
Pence's first trip to South Korea carries personal meaning as well.
While Washington had a "wide array of tools" at the President's disposal, "for this particular case, if they (North Korea) took the time and energy to launch a missile that failed, we don't need to expend any resources against that", said the adviser.
McMaster met Afghan officials in Kabul Sunday to discuss strategy in the Middle East, days after the USA dropped the "mother of all bombs" on an underground tunnel network in Afghanistan, reportedly killing dozens of ISIS members. Recent satellite imagery suggests the country could conduct another underground nuclear test at any time.
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