Japanese Prime Minister Shinzo Abe says he believes Donald Trump is a leader in whom he can have great confidence after meeting with the US president-elect in New York on Thursday.

Abe described Trump's first meeting with a world leader as cordial but offered few details of their discussion.

"I am not going to dive into details or specifics about today's discussion with President (elect) Trump. However, I do believe that without confidence between the two nations, the alliance would never function in the future. And as an outcome of today's discussion I am convinced that Mr Trump is a leader in whom I can have great confidence." Japanese Prime Minister Shinzo Abe said.

Abe described the talks as candid, under a warm atmosphere. The Japanese leader was seeking reassurances about the future of U.S.-Japan security and trade relations.

Trump's campaign rhetoric caused much unease when he said America's allies should pay more for help from U.S. forces.

Trump also said during the campaign that he opposes the Trans-Pacific Partnership, a trade pact involving 12 Pacific-rim nations.

Abe said the two leaders will meet again and hold "wider and deeper talks".