After the hastily arranged 90-minute meeting at Trump Tower in Manhattan, Abe called Trump a trustworthy leader, although he said he would not disclose details of the conversation because the talks were unofficial.
The Republican president-elect will succeed Democratic President Barack Obama on Jan. 20.
Abe characterized the talks to reporters as "candid" and added they were held in a "warm atmosphere."
He said he had agreed to meet again with Trump in order to hold "wider and deeper talks."
Japanese Finance Minister Taro Aso told reporters on Friday in Tokyo that it was beneficial for Abe to meet Trump before he becomes president, given that Japan-U.S. relations were vital to both countries.
The conversation came as Japan's leadership was nervous about the future strength of an alliance that is core to Tokyo's diplomacy and security.
Abe and other Asian leaders were alarmed at Trump's pledge during his election campaign to make allies pay more for help from U.S. forces, his suggestion that Japan should acquire its own nuclear weapons and his staunch opposition to the Trans-Pacific Partnership trade deal.
