Their talks will cover Japanese investment in the US, following recent criticism from Mr Trump.
Japan’s prime minister says he hopes to build a « relationship of trust » with Donald Trump, as he begins a US visit.
Addressing business leaders, Shinzo Abe said economic ties benefited both sides and urged a « new era » of co-operation.
President Trump has previously taken issue with the US trade deficit with Japan, and has threatened to impose a tariff on Japanese carmaker Toyota.
The two leaders, who are now meeting at the White House, are due to discuss the US military commitment to Japan.
The US army maintains a significant presence on the island of Okinawa and elsewhere in Japan, a key security lynchpin in the Asia-Pacific region.
« I wish to firmly build a relationship of trust at the leadership level with my visit to the United States, and to show to our people and the world the unwavering alliance between Japan and the United States, » Mr Abe said at the start of his two-day visit.
« I’m hoping in earnest that my visit this time will usher in a new era of our bilateral relations, » he added.
He also described US-Japanese economic and trade ties as a « truly win-win relationship ».
Last month Mr Trump tweeted that Toyota was planning to build a plant in Mexico that would produce cars bound for the US, saying: « NO WAY! Build Plant in U. S. or pay big border tax. »
Toyota responded saying their production and employment levels in the US would not decrease.
Mr Trump has also previously criticised Japan for not buying enough US-made cars, in comments reminiscent of the 1980s trade friction between the two economic powerhouses.
He has also named Japan as one of several countries contributing to the US trade deficit, and accused it of currency manipulation.
The Japanese government has in turn taken pains to point out that as a top US direct investor, Japan has created hundreds of thousands of US jobs, and that other countries such as China have far larger trade surpluses than Japan.
Chief cabinet secretary Yoshihide Suga said last month it was « absolutely not the case » that Tokyo was devaluing the yen to benefit its exporters, and that it had embarked on monetary easing to stabilise prices domestically.
Mr Abe is expected to discuss trade issues with Mr Trump, who withdrew the US from the controversial 12-nation Trans-Pacific Partnership (TPP) trade pact which Mr Abe had lobbied hard for.
Japan will also look for a guarantee of a US military commitment to maintain stability in the region, as China continues its ascent as a military superpower while North Korea develops its nuclear programme despite UN sanctions.
Following their talks, Mr Trump will be hosting Mr Abe and his wife at his Mar-a-Lago Club in Florida, where the two leaders will play golf.
They last met in November when Mr Abe visited Mr Trump in New York shortly after the latter won the US presidential election.
Mr Abe is the second foreign leader Mr Trump has met since taking office, after Britain’s PM Theresa May.
