The Japanese Foreign Ministry declined to comment on the documents, but it said in a statement that “a broad agreement is within reach.” Foreign Minister Fumio Kishida is preparing to work out the final details with Cecilia Malmstrom, the European trade commissioner, and a deal could be announced as early as next week, according to the Japanese public broadcaster NHK.

The European Commission would not comment on the document. In an emailed statement, the commission said, “The negotiators are now in permanent contact at all levels to conclude an agreement as soon as possible.”

“In the current international environment, an ambitious E.U.-Japan deal would send a powerful signal to the rest of the world that two of the largest economies are resisting protectionism and that openness to trade and investment remains one of the best tools to harness and shape globalization and create more economic growth and jobs,” the statement said.

The rest of the world is moving ahead with trade alliances as the Trump administration pushes a nationalistic “America first” agenda. Mr. Trump has called for higher tariffs in a broad defense of American manufacturing jobs against low-cost imports.

Just days into his presidency, Mr. Trump pulled the United States out of the 12-nation Trans-Pacific Partnership deal brokered by his predecessor, as he declared an end to the era of big multinational trade agreements. While Commerce Secretary Wilbur Ross has said the United States is open to reviving its own stalled trade talks with Europe, Mr. Trump has seemed wary, complaining on Twitter of America’s “massive” trade deficit with Germany.

“It puts the U.S. on the back foot,” said Joshua P. Meltzer, a senior fellow at the Brookings Institution and a former senior trade negotiator for Australia. Under Mr. Obama, he said, American businesses were on their way to improving their positions in the Asian and European markets.