It comes as Mr Trump and his allies dismiss reports that his transition to the White House is in chaos
Donald Trump will sit down for talks with Japan's Prime Minister Shinzo Abe later - the US President-elect's first face-to-face meeting with a foreign leader.
The Japanese PM will likely seek reassurances Mr Trump remains committed to the US-Japan security alliance in the Asia-Pacific region.
Japan and South Korea were rattled when during his campaign the billionaire businessman said he would demand allies such as the two nations contribute more to the cost of basing American troops in their countries.
As he left Japan, Mr Abe told reporters he was looking forward to meeting Mr Trump and establishing trust in their new relationship.
"The Japan-US alliance is the axis of Japan's diplomacy and security," he said.
"The alliance becomes alive only when there is trust between us. I would like to build such a trust with Mr Trump."
Mr Abe will be dropping by on his way to Peru, where world leaders are gathering for an Asia-Pacific trade summit.
Mr Trump also made it clear during the presidential race that he is hostile to the kind of free trade deals that tend to be the focus of the annual Asia Pacific Economic Cooperation forum.
He has also singled out group members China and Mexico in a populist campaign in which he said he would stand up for displaced American workers.
That has likely changed the tone and the agenda of a meeting that was expected to be part of a valedictory tour for US President Barack Obama - his last international summit before he hands over the keys to the White House to Mr Trump on 20 January.
Chinese President Xi Jinping and Russian President Vladimir Putin are among those attending the summit.
On the domestic front, Mr Trump has dismissed reports his transition is in chaos - saying his cabinet selection process "is going so smoothly".
US media reports had suggested there is infighting in the President-elect's team - with one insider reportedly describing it as a "knife fight".
"The disagreements highlight the dilemma faced by Trump, who is now torn between a campaign promise to shake up Washington and the need to build a national security team with policy experience," CNN reported.
But Mr Trump's campaign manager, Kellyanne Conway, said: "It's false to say it's not going well.
"Everything up there is very smooth. I know the President-elect himself is very happy with how the transition is going."
Newt Gingrich, a supporter of Mr Trump and a former Speaker of the House of Representatives, added: "Nobody should kid themselves, this will be President Trump's administration.
"He will make all the major decisions - that's how he has run his empire when in the private sector. It works for him. He did after all, beat 15 other Republicans before beating Hillary. He probably has some confidence in himself."
In an Apprentice-style tweet, Mr Trump himself asserted: "Very organized process taking place as I decide on Cabinet and many other positions. I am the only one who knows who the finalists are!"
However, his appointments are causing deep concern on both the left and right of American politics.
Most controversial is the appointment of Steve Bannon, formerly chairman of controversial right-wing propaganda and news website Breitbart, who will be his chief strategist,
Balancing his appointment, Reince Priebus will become White House Chief of Staff.
Texas Senator Ted Cruz, who Mr Trump dubbed "Lyin' Ted" during the Republican primaries, has been spotted at his office at Trump Tower in Manhattan, and is reportedly being considered to serve as the US Attorney General.
Former New York mayor Rudy Giuliani is tipped for Secretary of State.