TOKYO — As every Japanese knows, when you travel abroad, you must bring home some “omiyage” — souvenirs.

But after Prime Minister Shinzo Abe’s first day visiting President Trump at his Mar-a-Lago estate in Palm Beach, Fla., the Japanese public is wondering whether their leader, embattled at home by influence-peddling scandals, might return to Japan with the diplomatic equivalent of an “All I Got Was This Lousy T-shirt.”

When Mr. Trump and Mr. Abe appeared before reporters in Palm Beach on Tuesday, the American president declared that “Japan and ourselves are locked, and we are very unified on the subject of North Korea” and that Japan and the United States “have never been closer than they are right now.”

But as the two leaders were meeting, news emerged that Mike Pompeo, the C.I.A. director, had been to North Korea this month for secret meetings with its leader, Kim Jong-un. There, Mr. Pompeo was laying the groundwork for a meeting between Mr. Trump and Mr. Kim to discuss the North’s nuclear program.