Earlier on Monday, National Security Adviser General HR McMaster said the USA and its allies agreed that the North Korea "problem is coming to a head". The White House adviser said Tuesday's talks would not prescribe a free-trade deal but talks might eventually lead to such negotiations.
North Korea has tested five nuclear missiles under leader Kim Jong-Un, according to the New York Times.
Labelling North Korea's failed missile test at the weekend a "provocation", Mr Pence said the regime "would do well not to test [President Trump's] resolve or the strength of the armed forces of the United States in this region".
For the past quarter century, the United States and South Korea have tried to convince North Korea to abandon its nuclear aspirations.
The vice president earlier visited a military installation near the DMZ, Camp Bonifas, for a briefing with military leaders at the joint U.S.
The high-profile failure came as a powerful US aircraft supercarrier approached the Korean Peninsula and as thousands of USA and South Korean troops, tanks and other weaponry were deployed in their biggest-ever joint military exercises.
North Korea launched their fifth nuclear test April 15 after a day of military parades, but the weapon exploded almost immediately, according to CNN.
Pence said in Seoul on Tuesday the Trump administration would review and reform the 5-year-old free trade agreement with South Korea.
At a press conference in NY on Monday, Kim In Ryong, North Korean ambassador to the UN, accused the United States of disturbing global peace and stability, using "gangster-like logic" and being "hell-bent on unsafe saber rattling in South Korea". THAAD, or Terminal High Altitude Area Defense, is a weapon created to intercept short-and-medium-range ballistic missiles as they begin their descent to their target.
"If the United States dares opt for a military action (.) the DPRK is ready to react to any mode of war desired by the Americans", Kim told a news conference at UN headquarters in NY.
The BBC reported Han also said North Korea believed its nuclear weapons protect it from the threat of military action by the United States.
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Pence reassured Prime Minister Shinzo Abe on Tuesday that the US considers its alliance with Japan to be a cornerstone of security in the region.
Pence, sporting a brown bomber jacket, made his comments during an announced visit to the tense Demilitarized Zone that serves as a buffer between the stretch of land dividing North and South, allowing him to literally stare at North Korean soldiers from afar as he offered his vaguely threatening remarks.
Several times in recent weeks, President Trump has used his Twitter account to admonish the North Koreans.
Another official, speaking on condition of anonymity to discuss an intelligence matter, said the missile was a Scud variant that the US calls a KN-17.
The US and South Korea will push for early deployment of the US Terminal High Altitude Area Defence (Thaad) anti-missile system to guard against the North, he said.
He described the relationship as one of "totally seamless cooperation".
"Japan, though, is unwilling to give up on the TPP, and it's organizing other member nations to move ahead without the U.S".
China has appeared increasingly frustrated with its North Korean neighbour and ally, speaking out against its weapons tests and supporting United Nations sanctions, while repeatedly calling for talks.
Robert Kelly, an associate professor of political science at Pusan University in South Korea, speaking on Sunday night, said that the failed missile test was "probably the best possible outcome", because the North Koreans "got to say that they made trouble", while "the Americans were sort of let off the hook of having to find some kind of response".
Almost 30,000 American soldiers are stationed in South Korea, and military exercises on land and sea in the area are frequent, according to The Times.