Mr McMaster gave the blunt assessment that Pyongyang's stance "just can't continue" after its failed missile launch on Sunday.
Pence arrived in the region a day after North Korea celebrated the birth anniversary of the country's late founder with a military parade showing off missiles and military hardware.
"It appears today's launch was already scheduled for re-launching after the earlier test-firing", said Kim Dong-yub, a military expert at Kyungnam University's Institute of Far Eastern Studies in Seoul.
Despite this latest failed launch, concern from the South Korean military - still technically at war with the North and always on alert - was swift.
Washington wants to achieve security "through peaceable means, through negotiations".
Speaking at the DMZ, Pence said the U.S. "has always sought peace through strength and my message here today. standing with courageous soldiers from the Republic of Korea is a message of resolve".
"It's time for us to undertake all actions we can, short of a military option, to try to resolve this peacefully", he said on ABC's This Week programme.
The U.S. Pacific Command said the missile "blew up nearly immediately", adding the type of missile was being analysed.
Vice President Mike Pence's visit to South Korea last weekend was another clear signal that the world's greatest power is committed to confronting the North's behavior - as was the dispatch of a United States carrier battle group. Neither military knew what kind of missile was sacked.
He has repeatedly said if China, North Korea's dominant trading partner, is unwilling to do more to pressure the North, the US might take the matter into its own hands.
His visit comes amid escalated tensions on the peninsula, with heated rhetoric from both North Korea and the US.
Canadian DeLaet, Donald share lead after 2 rounds at RBC Heritage
Kevin Kisner had the round's best score, a 7-under 64, and was among six players four strokes behind the leaders. Donald had a brilliant second shot on the par-5 No. 2 (his 11th hole).
Trump has ordered a navy strike group flagshipped by a nuclear-powered aircraft carrier to head to the region as a show of force as his officials assess tougher economic sanctions as well as military options against the North.
He warned that North Korea's goal with its nuclear program is "more ambitious" than just seeking "regime survival". Recent satellite imagery suggests the country could conduct another underground nuclear test at any time.
Kim Jong Un has overseen three nuclear tests and a string of missile and rocket launches since taking over after the death of his father, dictator Kim Jong Il, in late 2011.
In August past year, a submarine-launched ballistic missile tested from Sinpo flew 500 kilometres (300 miles) towards Japan.
He wants to demonstrate USA economic interest in the region after Trump abandoned the Trans-Pacific Partnership (TPP), a trade deal negotiated by former President Barack Obama.
Impoverished North Korea and the rich, democratic South are technically still at war because their 1950-53 conflict ended in a truce, not a peace treaty.
A White House foreign policy adviser traveling with Pence said no USA response to the missile launch was expected because there was no need for the U.S.to reinforce the failure.
He also indicated that new anti-missile measures like the THAAD system could be fast-tracked.
Washington sees North Korea's pursuit of nuclear weapons and ballistic missiles as a threat to world security and to its Asian allies, Japan and South Korea.
Hours later, Pence landed for talks on the North's increasingly defiant arms program.
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