After easing into his Asian debut with golf, President Donald Trump sat down for a meal of American beef and tomato sauce with the Japanese president.

The notoriously picky eater arrived in Japan yesterday, where Prime Minister Shinzo Abe made sure to have his chef armed with tomato sauce to keep Mr Trump happy.

From the moment Marine One landed on the Kasumigaseki Country Club's driving range, Mr Abe rolled out little touches to make Mr Trump feel welcome.

Donald Trump, his wife Melania, and Shinzo Abe and his wife Akie arrive at the Ginza Ukai Tei restaurant to have a dinner in Tokyo. (AAP)

He presented the US with a hat embroidered with the words "Donald and Shinzo: Make Alliance Even Greater" – a play on Mr Trump’s 2016 election campaign theme.

The two then shared a meal of American beef, passing up the region's famous Kobe beef. Mr Trump ordered his beef "well done" and drenched it in tomato sauce.

The two leaders, who have struck up an unlikely but easy rapport, shared a casual lunch and played nine holes at the Kasumigaseki Country Club, joined by professional golfer Hideki Matsuyama.

White House officials said Mr Trump has spoken with Mr Abe by phone more than any world leader, aside from British Prime Minister Theresa May.

"The relationship is really extraordinary. We like each other and our countries like each other," Mr Trump said before dinner with Mr Abe, who for this meal did show Mr Trump traditional cuisine with teppanyaki.

"And I don't think we've ever been closer to Japan than we are right now."

Donald Trump, right, Japanese Prime Minister Shinzo Abe, left, and Japanese golfer Hideki Matsuyama, centre in blue, play golf at the Kasumigaseki Country Club. (AAP)

Mr Abe told reporters after the golf session that the two could talk frankly in a relaxed atmosphere while out on the course. He said they were able to "carry out in depth discussion, at times touching on various difficult issues".

Today, Mr Trump will meet with anguished families of Japanese citizens snatched by Pyongyang's agents.

The meeting promises to elevate these heart-wrenching tales of loss to the international stage as he hopes to pressure North Korea to end its provocative behaviour toward American allies in the region.

North Korea has acknowledged apprehending 13 Japanese in the 1970s and 1980s, but claims all those captives have died or been released. But in Japan, where grieving relatives of the abducted have become a symbol of heartbreak on the scale of American POW families, the government insists nearly 50 people were taken — and believes some may be alive.

Mr Trump and Mr Abe golfing in Japan. (AAP)

Mr Trump has delivered harsh denunciations of the renegade North Korean leader Kim Jong Un, belittling him as "Little Rocket Man" and threatening to rain "fire and fury" on his country if the belligerence continues. But Mr Trump also has begun highlighting the plight of the North Koreans.

"I think they're great people. They're industrious. They're warm, much warmer than the world really knows or understands," Mr Trump told reporters on Air Force One while flying to Japan yesterday.

"And I hope it all works out for everybody."

Also on the agenda during Mr Trump's second day in Asia: an audience with Emperor Akihito, a sit-down with Prime Minister Shinzo Abe and a state dinner.