The talks came amid news that CIA Director Mike Pompeo had recently traveled in secret to North Korea to meet with Kim ahead of a U.S. But Mr. Trump made news Tuesday when he said the US and North Korea have had "direct" talks at "extremely high levels," fueling questions.
Trump said Wednesday from his Florida resort that Pompeo and Kim got along "really well, really great". "We'll iron those out, hopefully".
"Japan and ourselves are locked, and we are very unified on the subject of North Korea", Trump said Tuesday.
The Trump-Abe summit has played out amid growing tensions between the two countries over North Korea and trade.
That meeting led to a series of developments which ultimately resulted in next week's summit between the two Koreas and the meeting between Trump and Kim, which is expected to happen in May or June.
Previously, they have welcomed any help and attention from the USA government, and Iizuka's specific requests underscore the families' desperate hopes. But one area where bilateral relations have remained lackluster is trade, and Japan is not alone in this regard.
The two couples went on a "friendship walk" around Mar-a-Lago on Tuesday, when the Abes arrived for a two-day summit.
First lady Melania Trump is giving her Japanese counterpart a tour of a Palm Beach mansion. And Trump had said earlier in the evening that officials had identified five possible venues for the summit. But he said the current trade deficit between the two countries is too high for him to offer an exemption now.
Trump is set to meet with the North Korean dictator later this year, no specific date or location has been released by the White House.
Trump took credit for the inter-Korean talks, saying, "Without us and without me, in particular, I guess you would have to say, they wouldn't be discussing anything".
The summit with Abe comes as the President prepares for historic talks with Kim, a prospect that Abe has warned will come with risks.
"As I've said before, there is a bright path available to North Korea when it achieves denuclearization in a complete and verifiable and irreversible way", he added.
Prime Minister Abe hoped to reverse his decision to impose new steel and aluminum tariffs on Japan.