Pence's trip to the flashpoint frontier underscored the US' shifting policy towards the isolated state after years of nuclear and missile tests carried out in defiance of the international community.
The latest launch - which failed when the missile blew up seconds after blast off, according to US and South Korean officials - came a day after the North held a defiant massive military parade in Pyongyang showcasing nearly 60 missiles, including a suspected new intercontinental ballistic missile.
Washington wants to achieve security "through peaceable means", through negotiations," Pence said at the village of Panmunjom inside the Demilitarised Zone (DMZ).
"But all options are on the table as we continue to stand shoulder to shoulder with the people of South Korea."
Pence, speaking at Freedom House, a few metres from the military demarcation line that he described as a "frontier of freedom", said America's relationship with South Korea was "ironclad and immutable".
"The people of North Korea, the military of North Korea should not mistake the resolve of the United States of America to stand with our allies," Pence said, adding that "the era of strategic patience is over" and expressed hopes that China would "do more" to help solve the problem.
Rising tensions
Tensions between Pyongyang and Washington have soared in recent weeks, as a series of North Korean weapons tests have wrought ever-more bellicose warnings from Donald Trump's administration.
The new and inexperienced US president has indicated he will not allow North Korea to develop an intercontinental ballistic missile capable of delivering a nuclear warhead to the western United States.
Pyongyang insists it needs a powerful arsenal - including atomic weapons - to protect itself from what it says is the ever-present threat of invasion by hostile US forces.
A top White House foreign policy adviser on Sunday became the latest Trump official to warn that while diplomatic pressure was preferable, US military action is very much on the table.
"We have a wide array of tools at disposal for the president should he choose to use them," the official told the AFP news agency.
Speaking on Sunday before a handful of the 28,500 US military personnel stationed in South Korea, Pence denounced the latest North Korea test as a "provocation".
The North has a habit of test-firing missiles to mark major dates such as Saturday's 105th anniversary of the birth of the nation's founder Kim Il-Sung, or as gestures of defiance when top US officials visit the region.
South Korea's foreign ministry said that by conducting the latest test just a day after displaying a series of missiles, "North Korea has threatened the whole world".
After visiting the DMZ, Pence is expected to hold talks with South Korea's Acting President Hwang Kyo-Ahn in Seoul.
This is Pence's first visit to South Korea - part of an Asia tour that also includes stops in Japan, Indonesia and Australia.
/Al Jazeera/
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