DETROIT — President-elect Donald J. Trump is not attending the country’s premier auto show here. But his vow to impose tariffs on imports from Mexico has changed the focus of the show from what new vehicles are on display to where they are made.

More than anything, said Sergio Marchionne, the chief executive of Fiat Chrysler, the industry needed to know what was going to happen with the North American Free Trade Agreement, which allows for a free flow of trade between the United States and Mexico.

“We need a clear indication of how the U.S. administration plans to deal with Nafta,” Mr. Marchionne said at the auto show. “We’re just waiting for clarity.”

Mr. Trump has made the auto industry a frequent target, attacking automakers for selling Mexican-made vehicles in the United States. In response, some automakers have somewhat changed their strategy.

Ford said on Monday that it would produce a new pickup and sport utility vehicle in a factory that is losing car production to Mexico. Fiat Chrysler announced on Sunday that it would invest $1 billion and create 2,000 jobs in the United States.

After the announcements from Fiat Chrysler and Ford during the auto show, Mr. Trump reversed course. He thanked the companies for commitments to add jobs and products at plants in Michigan and Ohio and took credit for the decisions.

“It’s finally happening,” Mr. Trump wrote on Twitter in reference to the job growth, adding, “Thank you Ford & Fiat C!”

What is unclear, though, is where the auto industry will head from this point. And that was a running discussion in the first two days of the sprawling Detroit auto show, which opened on Sunday and is usually known far more for talk about engines than economic policy.

Mr. Marchionne, for example, said that although Fiat Chrysler was eager to add jobs and production in the United States, the company was less certain about further investments in Mexico.

“The reality of the Mexican auto industry has been tooled up to try and meet demand in the U.S. market,” he said. “If the U.S. market is not there, its reason for existence is on the line.”

Most major automakers have sizable manufacturing operations in Mexico that export to the United States and elsewhere.

Factories in Mexico are considered an integral part of global business strategies. But Mr. Trump has zeroed in on how investment in Mexico may be hurting the chances for job growth in America.

Ford, for example, recently canceled plans to build a factory in Mexico, a proposal that had been repeatedly criticized by Mr. Trump.

The president-elect also scolded General Motors for importing small Chevrolet Cruze hatchbacks from Mexico to augment its production of similar vehicles in the United States. But Mary Barra, the company’s chief executive, said it was too late to turn back on that decision.

“This is a long-lead business with high capital investments — decisions that were made two, three and four years ago,” Ms. Barra said at an auto show event promoting a new General Motors S.U.V.

However, Ms. Barra said G.M. was eager to work with the incoming Trump administration on issues related to manufacturing and job growth.

She said that she had spoken with Mr. Trump last week after his Twitter post about the Mexican-made Cruze and that she expected that dialogue to continue.

“There’s a lot of work to do,” Ms. Barra said. “When you really look at some of the things the president-elect has said, we have much more in common than we have different.”

Toyota, the Japanese automaker, has also been a recent target of Mr. Trump’s. At the show this week, the company is emphasizing the American character of its new cars.

The automaker has unveiled a new version of its Camry sedan, which is built at a factory in Georgetown, Ky., that employs 7,000 workers. The 2018 model that Toyota showed was sportier looking than previous versions and came with a suite of new safety features designed to stop the car and prevent accidents.

William D. Fay, general manager of the Toyota division, said the new Camry illustrated how much of an American company Toyota had become. Over the last three decades, it has built 10 assembly plants in the United States and has added engineering operations that develop many of the cars and trucks it sells here. The company’s American work force totals 136,000 people.

The Camry, the top-selling passenger car in the country, “spearheaded our Americanization story,” Mr. Fay said. “It is built for Americans by Americans.”

While executives are busy defending their companies’ manufacturing plans in the United States and elsewhere, industry analysts are trying to forecast what effect tariffs or curtailed Mexican production could have on the booming American market.

“Any policy that leads to closing well-functioning plants would be a waste of resources,” said Xavier Mosquet, an analyst with Boston Consulting Group. “Everybody is at full capacity.”

Questions are also being raised about imports into the United States from countries other than Mexico, and whether Mr. Trump will consider tariffs on vehicles built in Europe or Asia.

The entire debate is unsettling to automakers, some of which nearly collapsed in the last recession and are now enjoying strong comebacks.

They worry that policies enacted by the Trump administration could put the brakes on the American market, which last year set a second consecutive annual sales record, with 17.55 million vehicles sold.

But despite the president-elect’s disdain for some imported vehicles, some foreign automakers remain keenly interested in breaking into the American market.

At the show on Monday, Guangzhou Automobile Group, one of the largest automakers in China, displayed an S.U.V. that the company hopes to sell in America one day.

The company’s president, Qiujing Wang, said in an interview that its current plans were to enter the American market in 2019.

“We believe the American consumer will be interested in this car because of the styling and driving experience,” he said, adding that the company needed to thoroughly prepare its vehicles to meet United States safety regulations.

He expressed more concern that a Chinese-made vehicle would meet quality standards expected by American consumers than that tariffs could penalize imports.

“We believe the trade door will be open to Chinese products,” he said. “And the only condition to entering the U.S. market will be quality.”