The vice president spoke at a dinner after attending Easter church services with service members at the garrison.
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 United States aircraft carrier neared the Korean Peninsula.
"The North attempted to launch an unidentified missile from near the Sinpo region this morning but it is suspected to have failed", the South's Office of the Joint Chiefs of Staff said in a statement.
According to the adviser, the US had good intelligence both before and after the launch.
The timing of the test, coinciding with Pence's trip and a day after the military parade, would suggest deliberate defiance.
Pentagon of the United States has also confirmed the DPRK's missile launch, saying that the missile blew up nearly immediately and the type of missile is still being assessed.
The attempted blast-off near Sinpo, on North Korea's east coast, is believed to have failed shortly after launch, South Korean and United States officials said.
He noted to the soldiers that his late father, Edward, served in the U.S. Army during the Korean War and was awarded the Bronze Star on April 15, 1953 - 64 years to the day of the vice president's departure for South Korea.
Recent satellite images suggest its main nuclear site is "primed and ready", according to specialist USA website 38North.
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US Vice President Mike Pence used a visit to the heavily militarised border between the two Koreas on Monday to reiterate Washington's position that "all options are on the table" in dealing with Pyongyang, the day after the North's latest missile test. -South Korean military camp, which is just outside the 2.5-mile (4.02-kilometre)-wide DMZ.
One unnamed U.S. official said it was unlikely to have been an intercontinental missile, but investigations were continuing. "The president has no further comment", he said.
Having blasted Beijing throughout his presidential campaign for unfairly manipulating its currency, he tweeted Sunday: "Why would I call China a currency manipulator when they are working with us on the North Korean problem?"
He added, "In the coming weeks, months, I think there's a great opportunity for all of us ... to take action short of armed conflict so we can avoid the worst". "If they are unable to do so, the US, with its allies, will!" he tweeted Thursday.
The test came after North Korea displayed almost 60 missiles - including what is suspected to be a new intercontinental ballistic missile - at a parade on Saturday to mark the 105th birthday of its founder Kim Il-Sung.
Washington and Seoul will try hard to figure out what exactly North Korea fired. The launch Sunday came as speculation mounts about reported US plans for a pre-emptive strike.
The US said a ballistic missile exploded within seconds of the launch. This failure underlines that Saturday's huge parade in Pyongyang of rows and rows of missiles of different types does not mean the country yet has an effective nuclear arsenal.
The United States is considering pre-emptive strikes on North Korea's nuclear weapons sites, according to a published report.
"We are ready to hit back with nuclear attacks of our own style against any nuclear attacks", he said.
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