Eager to forge a bond with Tokyo's crucial ally, Abe was one of the first world leaders to court President-elect Trump.
Aerial drills conducted over South Korea by two US strategic bombers have raised tensions in recent days.
Prime Minister Shinzo Abe welcomed Trump to Japan Sunday with an effusive display of friendship that, in the days ahead, will give way to high-stakes diplomacy. The two men also met on the sidelines of an worldwide summit in Italy this spring and Trump hosted Abe in Florida.
Trump will also have a state call with the Imperial Family at Akasaka Palace during his visit.
And while there is worry in the region about Trump's unpredictable response to the threat posed by Kim Jong Un, Trump made clear he did not intend to tone down his bellicose rhetoric - including dubbing Kim Jong Un as "Little Rocket Man" - even while in an Asian capital within reach of the North Korea dictator's missiles.
The president's first stops are Japan and South Korea - frontline U.S. allies in the effort to force Pyongyang to abandon its nuclear programme, and the two countries with most to fear should a full-scale conflict break out.
His trip got off to a colorful start in Hawaii. He was taken by boat out to the USS Arizona Memorial, where lies the Second World War ship that was sunk by the Japanese during the Pearl Harbor attack in 1941.
"I hope we will be able to have thorough discussions about worldwide issues, including North Korea", Abe told a press conference shortly ahead of Trump's arrival.
"We'll be talking about trade", Trump told reporters at the White House on Friday.
Ballistic missile tests by North Korea and its sixth and largest nuclear test, in defiance of U.N. Security Council resolutions, have exacerbated the most critical global challenge of Trump's presidency. But I think we're going to have a very successful trip. "There is a lot of good will".
Trump said in a Fox News interview on Thursday that a meeting with Putin was possible on the sidelines of the Asia-Pacific Economic Cooperation (APEC) forum in Vietnam.
North Korea has acknowledged apprehending 13 Japanese in the 1970s and 1980s, but claims all those captives have died or been released.
Kremlin spokesman Dmitry Peskov had earlier acknowledged there was now no co-operation between Russian Federation and United States on North Korea. "It had better stop daydreaming of denuclearisation talks with us", said the commentary titled "Stop dreaming a daydream".
In Washington, a new analysis emerged from the Pentagon saying that a ground invasion of North Korea is the only way to locate and destroy, with complete certainty, all components of Kim's nuclear weapons program.
The two leaders met at the Kasumigaseki Country Club for a round of golf with Japanese star golfer Hideki Matsuyama.
President Trump kicked off his Asia tour Sunday with a warning that the USA will use its military might, if necessary, to fend off hostile threats.