"We appreciate the challenging times in which the people of Japan live with increasing provocations from across the Sea of Japan", Pence said after arriving from Seoul for talks with Abe.
The BBC's Stephen Evans in Seoul says United States policy now seems to be to persuade China to contain North Korea while keeping the economic and military pressure on.
Washington and Tokyo want to see "concrete results in the near term" regarding improvements in bilateral trade, the two countries said on Tuesday.
"We need to apply pressure on North Korea so they seriously respond to a dialogue" with the worldwide community, he said, urging China and Russian Federation to play more constructive roles on the issue.
Japan and the USA have outlined a path forward for economic talks between the countries.
"It is our belief by bringing together the family of nations with diplomatic and economic pressure we have a chance of achieving a freeze on the Korean Peninsula", Pence said.
"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 TPP was a "thing of the past" for the US, Pence reaffirmed on Tuesday. After taking office he immediately withdrew from the multi-lateral Trans Pacific Partnership (TPP) trade deal that was to include the U.S., Japan and ten other Pacific Rim countries, that together accounted for 40 percent of the world economy. Tokyo is wary of a two-way free trade agreement (FTA), fearing it would boost pressure to open up politically sensitive sectors such as agriculture.
US Vice-President Mike Pence says "all options are on the table".
One main reason for the press conference was to "categorically reject" the USA decision to hold an open meeting of the UN Security Council on April 28 on North Korea's nuclear program, which is expected to be chaired by U.S Secretary of State Rex Tillerson, AP quoted Kim as saying.
Trump wrote Sunday on Twitter that China was working with the United States on "the North Korea problem". Trump has in the past complained that Japan keeps its currency artificially low, though a Treasury Department report last week did not label Japan a currency manipulator. The issue was not expected to be raised in talks on Tuesday.More news: Cup win over Chelsea will leave them doubting title credentials, says Kane
Mattis struck an even tougher tone on North Korea in an interview with reporters traveling with him to Saudi Arabia.
Chinese sanctions alone will not immediately force North Korea to give up its nuclear weapons, and Washington also must provide a security guarantee, the editorial said.
Japanese Finance Minister Taro Aso speaks at a news conference during the G20 finance ministers meeting in Baden-Baden, Germany, March 17, 2017.
The envoy criticised the United States missile strikes that hit an air base in Syria last week, saying Washington was resorting to a "gangster-like logic" that its military action was proportionate and could apply to the Korean peninsula as well. The White House adviser said Tuesday's talks would not prescribe a free-trade deal but talks might eventually lead to such negotiations.
As Indiana governor, Pence saw firsthand the impact of Japanese automakers Toyota, Honda and Subaru, whose factories employ thousands of people in his home state.
"I've seen that the United States has reiterated it is willing to use political and diplomatic means to resolve this, as this is their first choice", he told reporters in Beijing.
IN is the top USA state for per-capita foreign direct investment from Japan, including higher-technology and better-paying manufacturing jobs, said Victor Smith, Pence's commerce secretary when he led the state.
Pence's advisers told reporters that he hopes to win better US access to Japanese markets and to attract more Japanese investment in the U.S.
Pence will take that message to upcoming stops this week in Jakarta and Sydney.
He said his country's "era of strategic patience" with North Korea was over.