The U.S. and Japan are still thrashing out details of a trade deal that President Donald Trump wants to sign this month, including the crucial issue of whether he'll refrain from imposing higher tariffs on imported cars, according to people familiar with the matter.

At the Group of Seven meeting in France last month, Trump celebrated what he called a "major deal" that he and Prime Minister Shinzo Abe would sign on the sidelines of the United Nations General Assembly, set to begin later this month in New York.

But people familiar with the talks said the leaders only agreed on the broad strokes of a trade deal. Negotiators are now finalizing many of the core elements, including how much Japan is willing to open its agriculture market to U.S. imports, cuts to industrial tariffs, and the treatment of digital trade — which could impact U.S. technology giants like Amazon.com Inc. and Alphabet Inc.'s Google.