WASHINGTON—The Trump administration plans to step up pressure on Canada by publishing this week the draft of a new North American Free Trade Agreement that includes only the U.S. and Mexico, while telling Congress the move is part of a broader strategy involving new trade talks with a list of countries likely to include Japan, Europe, the Philippines, and the U.K., according to people familiar with the plans.

The expected publication of a new Nafta agreement excluding Canada doesn’t necessarily signal that President Trump...