President Donald Trump's first trip to Asia began with a round of golf, a custom cap and a hamburger of American beef.

The president got a taste of home as Prime Minister Shinzo Abe welcomed him to Japan on Sunday with a display of friendship that will soon give way to high-stakes diplomacy. The two men have struck up an easy rapport.

The leaders played nine holes of golf at Japan's premiere course.

The low-key start was a prelude to the formal talks planned in Tokyo on Monday. Abe will be looking for a united front against North Korea and reassurances that the US will stand by its treaty obligations to defend Japan if attacked.

At Kasumigaseki Country Club, Abe rolled out little touches to make Trump feel welcome. He presented a hat that had a version of Trump's campaign theme, this time reading "Donald and Shinzo: Make Alliance Even Greater."

The two passed up the region's famed Kobe beef in favour of the American version, which is favoured by Trump, a famed picky eater.

Before the game, Trump delivered a speech in which he hailed Japan as a "crucial ally" and warned adversaries not to test America's resolve.

"Japan is a treasured partner and crucial ally of the United States and today we thank them for welcoming us and for decades of wonderful friendship between our two nations," Trump told American service members at Yokota Air Base on the outskirts of Tokyo.

Though Trump did not mention North Korea by name during the speech, the spectre of its weapons program will loom large throughout Trump's five-nation Asia trip. The president warned of the consequences of crossing what he called the "most fearsome fighting force in the history of our world".

"Together with our allies, America's warriors are prepared to defend our nation using the full range of our unmatched capabilities. No one - no dictator, no regime and no nation - should underestimate, ever, American resolve," he told the troops.

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 - which included dubbing Kim Jong Un as "Little Rocket Man" - even while in an Asian capital within reach of the North Korea dictator's missiles.

"There's been 25 years of total weakness, so we are taking a very much different approach" in dealing with the renegade regime in Pyongyang, he said, speaking to reporters on Air Force One.