Pence also said the U.S. would protect freedom of navigation and overflight in the South China Sea, where Beijing is entangled in territorial rows with several southeast Asia nations.
All-out war would ensue if the U.S. took military action, he said.
Unlike Obama, however, Trump has chose to confront this threat head-on, dispatching what he called a "very powerful" armada to the Korean Peninsula as a sign of strength and a show of solidarity with the United States' allies in the region, South Korea and Japan.
Mr Pence made the statement after talks in Tokyo with the Japanese Prime Minister Shinzo Abe.
The state's mouth-piece added the hermit kingdom was fully prepared for any attacks by the US.
However, North Korea said that the presence of U.S. troops in the Korean peninsula had created a situation in which "a thermonuclear war may break out at any moment". South Korea has convened a National Security Council meeting after the failed test, saying in a statement their government "condemns this serious threat on the Korean peninsula and overall worldwide society".
"If the USA is reckless enough to use military means it would mean from that very day, an all-out war", he said.
After meeting with Abe, Pence held talks with Japanese Deputy Prime Minister Taro Aso on a new U.S. -Japan "economic dialogue" to be led by the two. He did not comment on what might have caused the missile to fail. The tests have grown in sophistication each time, U.S officials said.
During the interview - which aired the morning after Trump live-tweeted the show - host Ainsley Earhardt raised the topic of North Korea. But no one was predicting what might come next.
Warriors' Matt Barnes (ankle) questionable after missing shootaround
They absolutely want him back as soon as possible, but the Warriors didn't just survive him being out - they thrived. The first is that these two teams are going to score a lot of points when they take the court during the series.
While Pence assured both South Korea and Japan of our continued support, in our article on April 11 we posed the following question: "Why should the United States bear the heavy financial cost and risk of involving American servicemen in an Asian war by maintaining a large military presence in Asia, when we could sell (not give, but sell) weapons to our allies so they can defend themselves?"
The US Navy's Carl Vinson strike group - consisting of an aircraft carrier and other warships - is on its way to the Western Pacific, Pacific Command said on Tuesday, following an order from President Donald Trump last week.
That kind of rhetoric has unnerved allies in Japan and South Korea, who would be at the sharp end of any North Korean response.
Pence told reporters Monday that Trump was hopeful China would use its "extraordinary levers" to pressure the North to abandon its weapons program.
In Moscow, the Russian foreign minister, Sergei Lavrov, told reporters on Monday that he hoped there would be "no unilateral actions like those we saw recently in Syria and that the USA will follow the line that President Trump repeatedly voiced during the election campaign".
For its part, China made a plea for a return to negotiations.
Foreign ministry spokesman Lu Kang said China opposed words or actions that could further raise tension.
The comments dash the hopes of Japanese policymakers, who have said they want to avoid use of the economic dialogue as a forum to discuss a bilateral FTA that may put them under U.S. pressure to open up highly-protected areas like agriculture.
Burns reported from Riyadh, Saudi Arabia and AP reporter Jonathan Lemire reported from NY.
Comments