United Auto Workers President Dennis Williams indicated his organization can work with President-elect Donald Trump on key trade issues even though the 81-year-old union supported his opponent and has a long history of backing Democratic Party politicians.

Mr. Williams said in Detroit on Thursday he is prepared to talk with Mr. Trump about trade and sees “a great opportunity” to “find some common ground.” Specifically, Mr. Trump has been a critic of the North American Free Trade Agreement, or Nafta, and the Trans-Pacific Partnership.

Mr. Williams also said he hopes Mr. Trump’s goal of increasing infrastructure spending will lead to additional projects.

The UAW has long opposed Nafta and said TPP is problematic, citing concerns about job loss for U.S. manufacturing workers. Membership in the UAW, which represents factory workers at Ford Motor Co. F -1.47% , General Motors Co. GM -0.37% , Fiat Chrysler Automobiles FCAU -0.08% NV and auto suppliers, has slipped since Nafta was forged in 1992 as Detroit car makers moved production to Mexico and bought components from parts makers outside the U.S.

“We agree Nafta either needs to be renegotiated or ended,” Mr. Williams said.

The UAW president’s comments underscore the broad appeal Mr. Trump had during his campaign, leading him to perform well in Rust Belt states initially expected to swing to Hillary Clinton. Mr. Williams estimates potentially more than a third of UAW members voted for Mr. Trump, and union officials detected anger within the rank-and-file in the days before the election.

The UAW initially expected lower support among its 400,000 members for Mr. Trump. The organization will conduct studies to get more concrete results. Mr. Williams said support may have been higher than 32% given the amount of people indicating they were undecided just before the election.

It is unclear if support from the UAW on trade will embolden Mr. Trump’s trade stance, which includes slapping a 35% tariff on certain products shipped to the U.S. from Mexico. He singled out Ford, which is moving small-car production from Michigan to Mexico in coming years, for criticism.

There were 926,000 jobs associated with motor vehicle and car parts production in October, according to preliminary figures provided the Bureau of Labor Statistics, a number that has been little changed since mid-2015. While auto manufacturing jobs are nearing the highest point since early 2008, hourly earnings of $21.32 an hour, on average, are slightly lower than a year-ago and nearly $1 lower than when industry employment was last this high.

While lower-cost assembly plants have been opened during the past decade by foreign companies such as Volkswagen AG and China’s Fuyao Glass Industry Group the UAW has agreed to concessions and contract terms that led to deep job losses and lower pay scales.

In late 2015, Mr. Williams signed contracts with Detroit auto makers that secured wage increases and phased out controversial tiered-wage systems in U.S. car factories.

For decades, anything that Ford, GM or Chrysler sold on dealer lots was considered an American car, while those built by all other auto makers were deemed foreign. Even as Toyota Motor Corp. , Nissan Motor Co. and others opened plants in Southern states and sourced more parts from U.S. parts factories, they continued to be considered outsiders.

The definition of an American car also is rapidly changing as Detroit auto makers rely more on Mexican labor to assemble vehicles, and purchase an increasing share of auto parts from factories outside the U.S. In 2017 model year cars sold by Ford, GM and Chrysler, an average of 51% of parts came from U.S. or Canadian sources, down from 52.5% in the prior model year.

The National Highway Traffic Safety Administration compiles data on vehicle content every model year. The latest data are preliminary and will be updated as more models are introduced for the coming model year.

Nearly two-thirds of the 64 models the Detroit auto makers have introduced for the 2017 model year will be built by UAW members. While less than 20% are assembled in Mexico, many so-called domestic cars have half of their parts content sourced from south of the U.S. border.

Write to John D. Stoll at john.stoll@wsj.com