But Mr. Trump has delighted in being unpredictable in trade negotiations, and it is unclear when or if a deal will be reached.

“I think there’ll be a deal maybe soon, maybe before the election, or one day after the election,” Mr. Trump told reporters aboard Air Force One as he flew to Mountain View, Calif., on Tuesday. “And if it’s after the election, it’ll be a deal like you’ve never seen, it’ll be the greatest deal ever and China knows that.”

As Mr. Trump has waged trade fights with China and other countries, governments like Japan, Canada, the European Union and Australia have moved ahead with free trade deals that exclude the United States, putting American companies at a competitive disadvantage.

That includes the Trans-Pacific Partnership, which lowered Japanese tariffs on a wide range of agricultural goods, including beef and dairy. Since Mr. Trump withdrew from the deal, Japan has ratified the agreement with the remaining 10 other members, giving products from Australia, New Zealand, Canada and Mexico better access to Japan than American producers have.

Details of Mr. Trump’s agreement with Japan have not been announced. But people familiar with the negotiations say the United States has secured more access for products like beef, pork, wheat and wine. In return, the United States will drop its tariffs for Japanese industrial goods, like machinery. Japan is seeking written assurances that Mr. Trump will not put tariffs on Japanese cars, but it is unclear whether the administration will agree.

Larry Kudlow, one of Mr. Trump’s chief economic advisers, told Japanese and American business leaders at the U.S. Chamber of Commerce on Tuesday that the United States was “on the verge of major breakthroughs” with Japan, as well as passing its North American trade deal and potentially in negotiations with Europe. He said the Japanese deal would also make advances in digital trade and e-commerce.

“We may be closing in on a terrific deal,” Mr. Kudlow said.

The administration is eager to claim that it has secured the gains of the Trans-Pacific Partnership without having to join an agreement that Mr. Trump called “a rape of our country.”