Mr. Trump has used the threat of 25 percent tariffs to pressure the global auto industry to locate more car manufacturing inside the United States. But government officials and industry executives say the administration has had little interest in opening yet another front in Mr. Trump’s global trade war. Such a move would compound economic damage from Mr. Trump’s trade fight with China, with economists estimating that car tariffs could raise the price of a new car by $1,400 to $7,000, weighing on American consumers.

As with other trade measures, White House advisers caution that the ultimate decision is up to Mr. Trump, who sees tariffs as a powerful tool to extract concessions from trading partners.

Mr. Trump announced in a proclamation in May that imports of foreign cars were harming the American car industry and posed a threat to national security. He gave other countries 180 days to address the problem through trade agreements with the United States. The measure was aimed primarily at narrowing the large trade surpluses in automobiles and auto parts that the European Union, South Korea and Japan run with the United States.

Japan has since signed a trade agreement with the United States that includes a verbal pledge by Mr. Trump not to proceed with a 25 percent tariff on cars and car parts. Canada and Mexico reached an agreement to avoid the tariffs as part of talks over a North American trade pact. And South Korea signed a revised trade deal with the Trump administration in September 2018 that it has long argued should shield it from tariffs.

But the ability of the European Union to avoid the tariffs has been less assured, given a volley of harsh words between the governments and only limited progress on a new trade agreement. Mr. Trump has repeatedly accused Europe of unfair trade practices that have allowed a flood of foreign cars into the United States, and efforts to resolve his concerns through trade talks have been stymied by disagreements about what should be included in a new pact.