Thursday's meeting at the Trump Tower in New York City came amid nervousness among Japan's leaders about the future strength of an alliance that is core to the country's diplomacy and security.
After the 90-minute conversation, Shinzo Abe said: "The talks made me feel sure that we can build a relationship of trust."
But he would not disclose specifics of the conversation because the talks were unofficial.
Abe and other Asian leaders were alarmed at Trump's pledge during his campaign to make allies pay more for help from US forces, his suggestion that Japan should acquire its own nuclear weapons and his staunch opposition to the Trans-Pacific Partnership trade deal.
Describing his conversation as "candid" and held in a "warm atmosphere", Abe said: "Alliances cannot function without trust. I am now confident that President-elect Trump is a trustworthy leader."