Mr Trump said the United States remained opposed to rejoining the Trans Pacific Partnership unless Japan and other parties to the trade pact offered "a deal that I can't refuse".
"Our country's position is that TPP is the best for both of the countries".
Notably, Trump did not exempt Japan from recently imposed steel and aluminum tariffs, as he did for other key US allies and trading partners. "Our country's position is that TPP is the best for both of our countries", he added, referring to the Trans-Pacific Partnership trade deal. Trump and Abe spent Wednesday morning golfing at one of the president's nearby golf courses.
He said Mr Pompeo had forged a "good relationship" with Mr Kim - whom the United States president was previous year calling "little rocket man" - and that the meeting had gone "very smoothly".
Still, Trump held out the slim chance that the US could return to the deal.
Trump said it was clear from their talks that the abductee issue is "one of the truly most important things on Shinzo's mind".
The director the White House's National Economic Council, Larry Kudlow, said on Tuesday the USA government wants Japan to open up its politically sensitive agriculture market, but this is a move Japan is likely to resist.
"I don't want to go back into TPP, but if they offered us a deal that I can't refuse on behalf of the United States, I would do it", he said. The leaders have bonded over "golf diplomacy" in both the USA and Japan, and US officials note that Trump has met with Abe more than any other foreign leader.
Flower memorial honoring former First Lady Barbara Bush moved
The Barbara Bush Foundation for Family Literacy raised more than $40 million for more than 1,500 literacy programs nationwide. In between Nancy Reagan and Hillary Clinton, Barbara Bush brought her own priorities to the job of first lady.
He also won Trump's support for securing the return of Japanese citizens abducted by North Korea. Trump said he wasn't.
Trump and first lady Melania Trump are set to host the Japanese delegations for dinner Wednesday evening.
Trump said at the press conference, "We will not repeat the mistakes of previous administrations". North Korea says eight others died and denies the remaining four entered its territory.
The U.S. itself is pushing for the release of three Americans.
Speaking on Thursday, Mr Moon said North Korea had said it was ready for "complete denuclearisation", and called for "bold imagination and creative solutions" to ensure the Koreas summit and the Trump-Kim summit would succeed.
The Trump-Abe summit began hours after reports that North and South Korea are negotiating a statement to formally end the war that began in 1950.
But he also urged caution, saying there should be "no reward" given to the North just because the reclusive country is responding to dialogue.
Still, the prime minister said that if the North takes "the right path" under 2002's Japan-North Korea Pyongyang Declaration, "there could be a possible path to settle the unfortunate past and to normalize diplomatic relations".