WASHINGTON — Thirty-six years ago, Japan lowered import tariffs on foreign automobiles to zero, ostensibly opening the world’s fourth-largest auto market to full international competition. Yet United States automakers say 93 percent of the cars on Japan’s well-tended roads are still made in Japan by Japanese companies.

Consumers there simply prefer their country’s cars, Japan has said.

Automakers in the United States, however, say something else has long been amiss: the systematic, intentional weakening of the yen by Japanese policy makers, which effectively raised the cost of all kinds of imports, autos included.

With bipartisan momentum building for a currency amendment to the trade bill, President Obama on Tuesday publicly backed a pledge by the leaders of the Senate Finance Committee and Representative Paul D. Ryan of Wisconsin, chairman of the House Ways and Means Committee, to complete a trade policy enforcement bill by next month.

That bill, which passed the Senate last week, contains its own tough currency measure, but Republicans are quietly working to water it down if not remove it altogether. Mr. Obama backed what he called “constructive tools to address unfair currency practices.”