It is a fraught time for both sides, and comes as Trump prepares to meet with North Korean leader Kim Jong Un, whose government has been openly antagonistic toward Japan.
Abe is struggling with declining popularity because of suspected cronyism scandals. Trump, whose White House is grappling with scandals and investigations of its own, may be hunting for a political win ahead of November midterm congressional elections.
Japan wants Trump to avoid a deal in which Pyongyang gives up ballistic missiles that can hit the U.S. mainland but keeps shorter-range missiles that threaten Japan. Abe also wants Trump to bring up Japanese citizens kidnapped by Pyongyang long ago.
At the summit with Trump on Tuesday and Wednesday, Tokyo is equally eager to avoid being pushed into talks on a two-way free trade agreement aimed not only at market access but at monetary and currency policies.