U.S. President Donald Trump kicked off the second day of a Japan visit on Sunday with a round of golf with Prime Minister Shinzo Abe, engaging in personal diplomacy aimed at smoothing tough discussions over differences on trade.

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

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

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

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 engaged in an expensive trade war that has pounded financial markets worldwide.

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

Donald Trump and Melania Trump arrive in Tokyo on Saturday. (Koji Sasahara/Associated Press)

"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, U.S. 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."

Trade deal unlikely

Fox News reported on Sunday that Trump planned to wait until after Japanese elections in July to push for a trade deal, and 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 programs. Trump said on Sunday he was not concerned about recent missile launches from North Korea and was confident that the country's leader, Kim Jong-un, would keep his promises.

U.S. President Donald Trump attends a Japanese business leaders event in Tokyo on Saturday. (Jonathan Ernst/Reuters)

After their golf game, Abe and Trump will attend a sumo tournament.

"I've always found that fascinating," Trump said about Japan's national sport during a meeting with 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, weighs 60-70 pounds and is being called the "President's Cup," according to a White House official.

Trump will be the first U.S. president to attend such a tournament, according to another U.S. official, and the first to present a cup in the ring.