Mr Abe told reporters the US President-elect was someone "in whom I can have great confidence"
Donald Trump has held talks with Japan's Prime Minister Shinzo Abe - the US President-elect's first face-to-face meeting with a foreign leader.
The meeting at Trump Tower in Manhattan was intended to smooth relations following Mr Trump's campaign rhetoric that cast doubt on the US-Japan security alliance in the Asia-Pacific region.
Speaking at a news conference after the meeting, which lasted about 90 minutes, Mr Abe said the talks had been "cordial" and "candid".
He also said he is confident of building a relationship based on trust with Mr Trump and agreed to meet him again to have "wider and deeper talks".
He told reporters the US President-elect was someone "in whom I can have great confidence".
Mr Abe said they talked about a number of issues but didn't elaborate on the contents of the meeting because the talks were unofficial.
Mr Trump made no comments following the private meeting.
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.
Japan and South Korea were rattled at the billionaire businessman's pledge during his election campaign to demand allies such as the two nations pay more for help from US forces based in their countries.
Mr Abe dropped by on his way to Peru, where world leaders are gathering for an Asia-Pacific trade summit.
Mr Trump also made it clear during the presidential race he is hostile to the kind of free trade deals that tend to be the focus of the annual Asia Pacific Economic Cooperation forum.
He has also singled out group members China and Mexico in a populist campaign in which he said he would stand up for displaced American workers.
That has likely changed the tone and the agenda of a meeting that was expected to be part of a valedictory tour for US President Barack Obama - his last international summit before he hands over the keys to the White House to Mr Trump on 20 January.
Chinese President Xi Jinping and Russian President Vladimir Putin are among those attending the summit.