Approval ratings for Trump's performance, according to many recent polls, is at record lows for a new commander in chief, but Pence said he "couldn't be more proud" to be a part of the current administration.
The White House hopes the talks in Tokyo will open doors in Japan for US -made products and attract Japanese investment for infrastructure projects in the United States.
The Navy said earlier that the carrier will arrive in the Korean region next week.
"The United States of America will always seek peace", he said.
Pence said after the meeting that Trump believes it is in America's interest to negotiate economic deals on a bilateral basis.
Vice President Mike Pence issued another strong warning to North Korea Wednesday.
Capital Economics said in a research note on Wednesday a renegotiated FTA would likely mean South Korea opens more of its economy to US companies but would "have a relatively small impact on the economy".
He said that the dialogue could lead to formal talks on a U.S. -Japan trade agreement, but that he would leave that decision to the future.
"The U.S. has been clear that we want to resolve this issue through the peaceful denuclearization of the Korean Peninsula", she added.
Trump in January signed an executive order to officially withdraw the US from the Trans-Pacific Partnership (TPP) trade deal.
U.S. Vice President Mike Pence says the U.S. will not relent until it achieves its objective of ensuring the Korean Peninsula is free of nuclear weapons.
A ship bell signaled his arrival Wednesday morning on the USS Ronald Reagan at the U.S. Yokosuka naval base south of Tokyo.
Pence told the ship's captain that he had spoken to President Donald Trump, and Trump "wishes he were here".
Japan is the second stop on a four-country trip that is taking Pence to South Korea, Indonesia and Australia.
"For now, both sides seem eager to downplay potential for conflict, with Aso repeatedly saying that trade friction has been vanquished in a 'new era of cooperation'". -South Korea free trade agreement began and there are too many barriers for US businesses in the country.
"We are with you 100 per cent", he told the premier.
In response to a question about whether Chinese officials would help convince North Korean leader Kim Jong Un to end his ballistic missile and nuclear testing, the vice president said Trump and Chinese President Xi Jinping had a frank discussion about a broad range of global issues, including the denuclearization of the Korean Peninsula when Xi visited Trump earlier this month in Florida.