Speaking to cheering military personnel at Yokota Air Base just west of Tokyo minutes after landing, Trump donned a bomber jacket and said "no one, no dictator, no regime and no nation should underestimate... American resolve".
"Every once in a while in the past, they underestimated us. It was not pleasant for them, was it?" roared Trump.
"We will never yield, never waver and never falter in defence of our people, our freedom and our great American flag."
According to the Washington Post, Pentagon officials have warned that the only way to locate and secure North Korea's nuclear weapons sites would be via a ground invasion.
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North Korea itself welcomed Trump to the region with a rhetorical volley via the ruling party newspaper Rodong Sinmun, warning a "spiritually instable" president against making "reckless remarks".
The president's first stops are Japan and South Korea -- frontline US 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.
Speaking to reporters on the plane, he announced he would likely be meeting Russian President Vladimir Putin during the tour, as the international community scrambles for a solution to the North Korean crisis.
"I think it's expected we'll meet with Putin, yeah. We want Putin's help on North Korea, and we'll be meeting with a lot of different leaders," said Trump.
He added that North Korea was a "big problem for our country and for the world, and we want to get it solved" but had kind words for its people.
The next stop was a golfing date with his "friend" Shinzo Abe, prime minister of Japan, with whom he enjoys a close personal relationship.
Trump joked with reporters on Air Force One that they should not believe him if he claims to outhit Hideki Matsuyama, one of the world's best players who joined the leaders on the course.
Abe also appeared to have enjoyed his nine holes, tweeting: "A round of golf with a marvellous friend (President Donald J. Trump), full of spirited conversation."
The Japanese leader has emerged strengthened from a crushing victory in a snap election and has firmly supported Trump in his policy of exerting maximum pressure on Kim, backed up with the threat of military force.
"I want to further cement the bond of the Japan-US alliance, based on our relations of trust and friendship with President Trump," Abe said as Trump arrived.
The pair later dined at a swanky restaurant in upmarket Ginza, with Trump telling reporters: "I don't think we've ever been closer to Japan than we are right now."
"Our relationship is really extraordinary."
After Japan, Trump travels to Seoul, where his relationship with President Moon Jae-In is noticeably cooler.
Trump labelled Moon's dovish approach to North Korea as "appeasement" on Twitter, a comment that did not go down well in Seoul's presidential Blue House.
Trump will speak to South Korean MPs but not follow the well-trodden path to the Demilitarized Zone dividing the Korean peninsula -- a visit derided in Washington as a bit of a "cliche".
Trump said before his trip that China could have a "big problem" with "warrior nation" Japan if the North Korea issue is not solved.
He then travels to an Pacific Rim summit in Vietnam before heading to a gathering of Southeast Asian leaders.
Some observers have fretted that a gaffe by the famously ad-lib president could send tensions rising on the peninsula.
"If Trump says anything that can provoke North Korea, it could send military tensions soaring again," said professor Koo Kab-Woo from the University of North Korean Studies in Seoul.