TOKYO (REUTERS) - US President Donald Trump kicked off the second day of a Japan visit on Sunday (May 26) with a round of golf with Prime Minister Shinzo Abe, engaging in personal diplomacy aimed at smoothing tough discussions over differences on trade, especially beef.

Mr Trump is unhappy with Japan's large trade surplus and is considering putting high tariffs on its auto exports if a bilateral trade agreement is not reached. The United States and China are also engaged in an expensive trade war that has pounded financial markets worldwide.

"Great progress being made in our trade negotiations with Japan. Agriculture and beef heavily in play," Mr Trump tweeted after arriving back in Tokyo from the suburban golf course where the two played 16 holes.

"Much will wait until after their July elections where I anticipate big numbers."

Mr Trump, dressed in a red pullover, and Mr Abe, wearing a blue blazer and white pants, smiled for photographers before taking off for their game.

Mr Abe's office later posted a selfie picture on the course with Mr Trump and Mr Abe smiling together. Mr Abe said in the post he hoped to make the Japan-US alliance "even more unshakeable".

Beef was also in play at lunch. The golf was followed by double cheeseburgers made with US beef, Japan's Foreign Ministry said in a statement.

"They deepened their friendship amid a cozy atmosphere," the statement added.

The President's state visit is meant to showcase the strength of the Japan-US relationship, but tensions over trade have provided a backdrop of uncertainty.

During remarks to business leaders on Saturday night, Mr Trump ribbed Japan over its trading edge while saying progress had been made.

"With this deal, we hope to address the trade imbalance, remove barriers to United States exports, and ensure fairness and reciprocity in our relationship. And we're getting closer," he said. "Just last week, US beef exports gained full access to Japan and to the markets in Japan for the first time since the year 2000. We welcome your support in these efforts, and we hope to have several further announcements soon, and some very big ones over the next few months."

US officials have played down prospects of any major progress on the President's trip.

The two leaders are also likely to discuss North Korea's nuclear and missile programmes. Mr Trump said on Sunday that he was not concerned about recent missile launches from North Korea and was confident that the country's leader, Mr Kim Jong Un, would keep his promises.

Mr Abe and Mr Trump will attend a sumo tournament in the afternoon.

"I've always found that fascinating," Mr Trump said about Japan's national sport during a meeting with Mr Abe in Washington last month. "So, in fact, we're having a trophy made in this country. We're going to give the trophy to the winner of the championship."

That trophy, now finished, is being called the President's Cup, according to a White House official. Photographs of the cup, which was on display in a Tokyo hotel lobby prior to the match, showed it topped by a bird with outstretched wings.

Mr Trump will be the first US President to attend such a tournament, according to another US official, and the first to present a cup in the ring. He is attending the final day of a 15-day tournament.