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US President Donald Trump, First Lady Melania Trump, Japan's Prime Minister Shinzo Abe, and his wife Akie Abe take part in a dinner at Trump's Mar-a-Lago estate.

Abe's meetings with Trump may provide a brief respite from his problems at home and could even stem the slide in his popularity. Important stuff to be discussed - North Korea, trade.

But he says the U.S.is still dealing with a massive trade deficit with Japan.

It was a disappointment for Japan.

But Abe spent much of Tuesday praising Trump's courage for agreeing to meet and suggested the two had already come to terms on several contentions issues.

Trump has made a regular habit of profiting from the presidency, which he began right after his inauguration with another visit from Japan's prime minister.

Mr. Trump also noted Pompeo's meeting with North Korean dictator Kim Jong Un, saying the two got along "really well".

Larry Kudlow, Trump's top economic advisor, has cautioned that while "Japan is a great friend and ally", there are "certain disagreements with respect to some of the trading issues, we'll iron those out hopefully".

Abe is struggling with languishing approval ratings and, while keen to stress a good relationship with Trump, would want to avoid being seen as a lap dog.

Pyongyang has acknowledged abducting 13 Japanese, while Tokyo maintains North Korea abducted at least 17 in the 1970s and 1980s to train agents in Japanese language and culture to spy on South Korea. North Korea says eight others died and denies the remaining four entered its territory.

US First Lady Melania Trump and Japanese First Lady Akie Abe arrive for a joint press conference of US President Donald Trump and Japan's Prime Minister Shinzo Abe at Trump's Mar-a Lago estate in Palm Beach Florida
Live stream: President Trump holds joint news conference with Japanese Prime Minister Shinzo Abe

The U.S. has also been pushing for the release of three Americans held captive.

Significant news from the day: Central Intelligence Agency director and Secretary of State nominee Mike Pompeo visited Kim Jung Un in North Korea last week and discussed the details of possible summit between the Trump and the North Korean leader whom Trump has dubbed "Rocket Man" in several chest-thumping tweets. I think there's a good chance of doing it.

"But that goes for other countries too", he said, vowing to "weed" the deficit down. "Our country's position is that TPP is the best for both of our countries", he added. Trump complains the US had a trade deficit with Japan a year ago of $56 billion.

Also on the docket will most likely be intense discussions about Trump's recently imposed tariffs on steel and aluminum.

The visit included a mix of business and pleasure.

One moment, Donald Trump is "apoplectic" about the gathering legal storm bearing down on his presidency that is threatening to lift the lid on his most guarded personal and business secrets.

The President could potentially face questions about all the competing demands on his attention during a press availability set for Wednesday evening with Abe. Trump has proven to be an unconventional commander in chief who prefers to live on his wits and seems perpetually mired in crisis.

They also partook in a round of "golf diplomacy" at the Kasumi Country Club when Trump visited Japan past year.

"He had a great meeting with Kim Jong-Un, and got along with him really well, really great".

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