Mr Pence arrived in Tokyo from South Korea, where he assured leaders of an "iron-clad" alliance.
A senior North Korean official has stated that his country will continue to test missiles in spite of worldwide condemnation. The trip so far has been dominated by US and allies' concerns about North Korea's nuclear and missile development efforts. "We are with you 100%", he said.
It appears Trump and other USA leaders are hoping China, long a patron of North Korea, will put pressure on dictator Kim Jong Un to back away from his military buildup.
Despite the tension, North Korea may carry out a sixth nuclear test soon, observers say.
"Just in the past two weeks, the world witnessed the strength and resolve of our new president in actions taken in Syria and Afghanistan", Pence had said, referring to missile strikes in Syria for deadly chemical attack and dropping of the mother of all bombs over IS hideout in Afghanistan.
Pence also said the United States would protect freedom of navigation and overflight in the South China Sea, where Beijing is entangled in territorial rows with several Southeast Asia nations.
The U.S. has been in discussion with China - North Korea's main ally - in attempts to apply pressure on North Korea's leadership to restrain their nuclear ambitions.
Asked whether he had ruled out the possibility of launching a military strike against North Korea, Trump said he did not wish to reveal his plans.
The economic talks started with Vice President Pence meeting Deputy Prime Minister Taro Aso in Japan, the second stop of his 10-day Asia tour.
North Korea-US tension is growing.
But economic policy advisers traveling with Pence reportedly said the trip is also aimed at reassuring Washington's allies that the current administration wants to boost trade in the Asia Pacific region particularly after the US withdrawal from the Trans-Pacific Partnership agreement.
Said Abe: "It goes without saying that it is a matter of paramount importance for us to seek diplomatic efforts as well peaceable settlements of the issue".
Americans "always have to be concerned" about the prospect of a thermonuclear war with North Korea, Donald Trump has said.
North Korea's deputy United Nations ambassador, Kim In-ryong, accused Washington on Monday of creating "a unsafe situation in which a thermonuclear war may break out at any moment". But it's becoming increasingly clear that President Trump might not know the name of North Korea's leader.
Tensions on the peninsula have ratcheted up in recent weeks amid saber-rattling from the United States and North Korea and analysts' warnings that North Korea is preparing for a sixth nuclear test. Trump administration officials in recent days have said the Obama administration's strategy of "strategic patience" is over.