"On a little bit lighter note", Trump said late Friday afternoon about the trip, "we will also be going perhaps to a sumo wrestling match". He will assume the throne after his father, Emperor Akihito, abdicates on April 30.
"In any case, we would like to proceed with the further negotiation that. we'll see a mutually beneficial outcome for both of our countries", Abe said through a translator.
"I think it can go very quickly", he said. "We have other things that we're talking about but I'll respond to that question at a later date".
Mr Trump said that they would discuss North Korea in the meetings immediately after their comments to the media.
Mr Trump struck a similarly optimistic tone, saying: "Ultimately, we have a chance to make a very good and long-term trade deal with Japan".
At the beginning of the talks, Trump showed his willingness to agree on a trade pact before his state visit to Japan from May 25.
Speaking to reporters with Abe at the White House, Trump said the two leaders plan to talk about a variety of security and economic issues, including "missiles and rockets and everything else".
Putin and Kim shake hands for the first time
Moscow has kept a relatively low profile as Kim embarked on what has been an audacious diplomatic journey over the past year. Russian Federation would like to gain broader access to North Korea's mineral resources, including rare metals.
Trump and Abe are also expected to discuss efforts to enhance trade and investment between the countries, according to the White House.
For his part, Abe said Japanese businesses have invested $23 billion in the USA since Trump assumed office in 2017 which supports 43,000 jobs.
The senior Japanese government official said the two leaders agreed that the governments would coordinate closely with each other and with South Korea to achieve the denuclearization of North Korea.
North Korea is also likely to come up in conversation, after the president's failed summit with North Korean leader Kim Jong Un.
Last year, the US President imposed tariffs on imports of Japanese steel and aluminium and threatened to slap levies on vehicles from Japan.
In June, the Japanese city of Osaka will be hosting the G20 summit, and Abe has strongly lobbied Trump to attend the gathering.
Though there has been plenty of speculation about the state of the Trumps' marriage, the First Lady has attempted in the past to put that to rest.
The president said he and Abe would head out very early on Saturday to play a "quick round of golf at a very lovely place on the Potomac River".