Shinzo Abe said he wants to “build confidence” and “work together for the prosperity and peace in the world”, before leaving for his visit.
The meeting comes in New York amid concern over the direction of foreign policy is the biggest ally of Tokyo.
Mr. Trump said Japan needs to pay more to keep US troops on its soil.
It also condemned a big trade deal struck by President Obama with Japan and other Pacific Rim countries.
The United States and Japan, key allies since the end of World War II, when the United States helped Japan rebuild its economy.
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Abe’s stop in New York on his way to the top of trade between Asia and the Pacific in Peru.
But Thursday’s meeting is not clear details, with a Japanese official as saying exactly where it will happen not entrenched.
“There has been a lot of confusion,” a Japanese official and the Reuters news agency.
Mr. Trump has also yet to determine the new cabinet and other positions. He denied that the move to the White House is in a state of chaos.
Mr. Trump spoke and Vice President-elect Mike Pence with 29 world leaders since the election, according to a statement from the transition team.
It was not immediately who else might be in the meeting with Mr. Abe unclear.
And are rarely held high-level talks in this formal context, Tokyo is keen to reduce uncertainty through a long delivery from power.
“We want to maintain the alliance with the United States during the transitional period,” said a senior official at the Japanese Foreign Ministry, Tetsuya Otsuru, when it was announced the meeting.
But there are some key points of difference between the two countries.
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