Pence reiterated that after years of North Korea testing the United States and its neighbors in East Asia with its nuclear ambitions, the US "era of strategic patience is over".
The missile fired on Sunday blew up nearly immediately, the Pentagon said.
On Monday Vice-Foreign Minister Han Song-ryol told the BBC that North Korea could test missiles on a weekly basis and warned of "all-out war" if the USA took military action.
But now, Pence will try to reassure his jittery hosts that those decades-old security commitments are ironclad, a necessity made more acute as tensions rise over Pyongyang's latest missile test and Washington's refusal to rule out military action against the regime.
He said Mr Jong-un would likely want to demonstrate his power by testing another nuclear weapon or missile as a result.
Abe also said Japan's government is drawing up contingency plans in case a crisis on the Korean Peninsula sends an influx of refugees to Japan. Over the weekend, he suggested in a tweet that part of the reason for the revised stance is that China could be helpful in deterring North Korea.
But Schilling said the ability to hack North Korea's missiles is overblown. Most importantly, if they want to resolve the crisis on the Korean peninsula, they need to hold six-party talks, in which North and South Koreas, the United States, Japan, Russia and China would participate.
United States officials say tougher sanctions could include an oil embargo, a global ban on North Korea's airline, intercepting cargo ships and punishing Chinese banks doing business with Pyongyang.
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Tensions have been escalating on the peninsula, with heated rhetoric from both North Korea and the US. And by that I mean, if they can put a warhead on top of a missile that can reach the United States, that's obviously a direct threat.
President Trump campaigned against the TPP, a long-negotiated multilateral trade deal that former President Barack Obama supported.
Pence struck a stern tone as he began talks with Abe and other Japanese leaders after arriving at a USA naval base from South Korea. They've been suspended since the last round collapsed in 2008 following a failed rocket launch in North Korea.
"North Korea would do well not to test his resolve, or the strength of the armed forces of the United States in this region", Mr Pence said at the press conference with South Korea's Acting President Hwang Kyo Ahn.
Trump on Monday told a reporter that North Korea has "got to behave" and, in remarks recorded for airing Tuesday on a Fox News program, contended that his presidential predecessors had "all been outplayed" by North Korean leader Kim Jong Un.
Trump wrote Sunday on Twitter that China was working with the United States on "the North Korea problem".
The country's deputy foreign minister, Han Song-Ryol, told the BBC that Pyongyang would continue to test missiles "on a weekly, monthly and yearly basis". However, North Korea didn't respond to Wu's request to visit Pyongyang, according to South Korea's Yonhap news agency. But then he ordered the unilateral missile strike against Syria, even after dismissing talk of deeper USA involvement in that nation's civil war.
"I think the USA has been clear that we want to resolve this issue through the peaceful de-nuclearization of the Korean peninsula", said Acting Assistant Secretary of State Susan Thornton.