Pence says North Korea's "provocation" is another reminder of the risks that USA and South Korean service members face every day "in the defence of the freedom of the people of South Korea and the defence of America in this part of the world".
Tensions on the peninsula have ratcheted up in recent weeks, amid tit-for-tat saber-rattling from the USA and North Korea and analysts' warnings that North Korea was preparing for a sixth nuclear test.
Sinpo, where the Sunday launch took place, is the site of a North Korean submarine base and where the North has tested the submarine-launched ballistic missile it is developing.
The demilitarised zone (DMZ) is a heavily mined, four-km-wide (2.5-mile-wide) strip of land lined with barbed wire running across the Korean peninsula, with soldiers on both sides in a continual eyeball-to-eyeball standoff.
Pence said at a fellowship dinner at US Army Garrison Yongsan in Seoul that the willingness of military members "to stand firm without fear inspires the nation and inspires the world".
A White House foreign policy adviser, briefing reporters on the plane that carried Pence to Seoul, was asked what steps China had committed to when President Xi Jinping met recently with Trump in Florida.
Pence emphasized the relationship between the US and South Korea.
China banned imports of North Korean coal on February 26, cutting off its most important export. "The problem will be taken care of".
Echoing the remarks of US Secretary of State Rex Tillerson on North Korea last month, Pence said the "era of strategic patience is over".
While But Mr McMaster stressed that the U.S. wanted to resolve the matter "peacefully", he also hinted that unannounced military action may also be considered by the US.
That missile flew about 60 km (40 miles) but what USA officials said appeared to be a liquid-fuelled, extended-range Scud missile only travelled a fraction of its range before spinning out of control.
USA prepared to 'utterly destroy' N Korea nuclear sites
In February, Trump told China's President Xi Jinping that the U.S. would, in fact, honor the decades-old policy. Recent satellite imagery suggests the country could conduct another underground nuclear test at any time.
U.S. officials told CNN they did not believe the missile had intercontinental capabilities, and blew up nearly immediately after launch. "The President has no further comment", said Mattis.
North Korea has conducted five nuclear tests, including two previous year. The rogue nation has conducted five nuclear tests and has claimed to have successfully "miniaturised" nuclear warheads, although that has not been independently verified.
If Sunday's missile launch leads to a nuclear test or an ICBM launch, there would be "a powerful punishing measure that North Korean authority can't endure", South Korean officials said.
A top White House foreign policy advisor on Sunday became the latest Trump official to warn that while diplomatic pressure was preferable, USA military action is very much on the table.
Trump may have been boxed in his campaign promises to go after China on trade and currency, and the reality of needing China's help on regional security problems, said Senator Jack Reed, Democrat of Rhode Island, also on NBC.
The officials weren't authorized to speak publicly on the results of the policy review and requested anonymity.
After South Korea, Pence is scheduled to travel to Japan, Indonesia and Australia during his 10-day trip.
Amid concerns the U.S. might launch a preemptive strike on North Korea, Pence said Washington would "closely consult" with Seoul "as we make decisions moving forward".
Into this tense environment, Pence made his first trip to the region since taking office in January.
We learned on his plane coming over that Pence's father, 2nd Lt. Edward J. Pence, Jr., served in the Korean War and was awarded the Bronze Star for his service.
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