Then President Donald Trump, right, talks with Tesla and SpaceX CEO Elon Musk at the White House in Washington, Feb. 3, 2017. (AP photo)

DETROIT — The United Auto Workers union has filed unfair labor practice charges against Republican presidential nominee Donald Trump and Tesla CEO Elon Musk after the two discussed on social media about Musk supposedly firing striking workers.

In documents filed Tuesday with the National Labor Relations Board, the union alleges that both men interfered with workers who may want to exercise their right to join a union. The NLRB said it would look into the charges, which are a request for the agency to investigate.

UAW President Shawn Fain, whose union has endorsed Democrat Kamala Harris, said in a statement that Trump is anti-labor.

“Both Trump and Musk want working class people to sit down and shut up, and they laugh about it openly,” Fain said.

Brian Hughes, a senior advisor with the Trump campaign, called the allegations “frivolous” and a “shameless political stunt” designed to erode Trump’s strong support among American workers.

The NLRB said it would investigate the complaints, one filed against the Trump campaign and the other naming Tesla Inc., the electric vehicle, battery and solar panel manufacturer based in Austin, Texas, and led by Musk.

The charges stem from statements made by Trump Monday night during a conversation between the two men on X, the social media platform Musk now owns. The former president spent much of the discussion that lasted more than two hours focused on his recent assassination attempt, illegal immigration and plans to cut government regulations.

But during a discussion about government spending, Trump praised Musk for firing workers who went on strike. The UAW contends this could intimidate workers for the Trump campaign or at Tesla who might want to join a union.

“You’re the greatest cutter,” Trump told Musk. “I look at what you do. You walk in and say, ‘You want to quit?’ I won’t mention the name of the company but they go on strike and you say, ‘That’s OK. You’re all gone.'”

Musk said, “Yeah,” and laughed while Trump was talking.

It wasn’t clear what employees Trump was referring to.

In June, eight former workers at SpaceX, Musk’s rocket company, sued the company and Musk, alleging he ordered them fired after they challenged what they called rampant sexual harassment and a hostile “Animal House”-style work environment at the company.

In addition, the NLRB determined that a 2018 Twitter post by Musk unlawfully threatened Tesla employees with the loss of stock options if they decided to be represented by a union.

Three judges on the 5th U.S. Circuit Court of Appeals in New Orleans upheld that decision, as well as a related NLRB order that Tesla rehire a fired employee, with back pay. But the full 5th Circuit later threw out that decision and voted to hear the matter again.

Sanjukta Paul, a law professor at the University of Michigan, said the UAW charges have real substance because the comments from Trump and Musk could “chill” efforts by workers to act collectively, including union organizing, or just getting together to improve working conditions.

“You’re approvingly describing, you’re wholeheartedly commending the blatant violation of our main federal labor statute,” she said. “It would constitute interference with protected rights.”

Marick Masters, a business professor emeritus at Wayne State University who follows labor issues, said the UAW’s move “puts the spotlight on Trump and attempts to put him on the defensive in terms of his attitude and demeanor toward unions.” He added that the union is watching Musk’s comments because it has targeted Tesla’s U.S. factories for organizing drives.