The administration has been racing to conclude the deal before Mr. Trump travels to New York next week, where he will meet again with Mr. Abe at the United Nations General Assembly.

A deal with Japan would give Mr. Trump a big talking point as he heads into his re-election campaign. Within days of assuming the presidency, Mr. Trump pulled the United States out of a multilateral trade deal — the Trans-Pacific Partnership — that would have given America greater access to Japan’s market and lower tariffs, along with the markets of countries like Australia, Singapore and Vietnam. The pact was welcomed by farmers but disliked by many Republicans and Democrats, and Mr. Trump said he would use America’s leverage to cement a better trade deal with Japan.

Since Mr. Trump pulled the United States out of the T.P.P., Japan and the pact’s 10 other remaining members have proceeded with ratifying the deal, and Japan has entered into a major trade agreement with the European Union.

While Japan initially resisted a bilateral trade deal with the United States and instead insisted that it rejoin the T.P.P., Mr. Abe ultimately agreed to one-on-one trade talks.

The Trump administration’s deal is likely to address a much narrower range of issues than the T.P.P. would have. American and Japanese officials have been eager to announce an “early harvest” deal that would buoy their partnership, as well as Mr. Trump’s chances at re-election, and then continue on to further negotiations on other industries.

The agreements on agriculture are unlikely to go beyond those Japan would have given to the United States under the terms of the T.P.P. Tokyo agreed to lower tariffs on a wide range of agricultural goods, including those from the United States, when it joined the T.P.P., and it has consistently said it would not offer the United States terms better than those enjoyed by the group’s member countries.

The new deal will not touch on many other areas of trade addressed in that agreement. Instead, negotiators envision tackling issues such as pharmaceuticals, energy and services in future talks.