Shawn Fain, the United Automobile Workers president, escalated pressure on the White House on Friday with a public invitation to President Biden to join workers on the picket lines in their growing strike against the nation’s leading automakers.

“We invite and encourage everyone who supports our cause to join us on the picket lines, from our friends and family all the way to the president of the United States,” Mr. Fain said in a speech streamed online.

The White House did not immediately respond to a request for comment. Mr. Biden’s re-election campaign posted on social media a video of Republican presidential candidates and Fox News anchors bemoaning his support for unions. The caption from Mr. Biden read: “Yes.”

Mr. Fain’s invitation comes a week into an expanding work stoppage by autoworkers at Ford, General Motors and Stellantis plants. The union president announced that the strike, which began last week at three plants in the Midwest, would expand to 38 more locations in 20 states across the country at noon on Friday. He said that talks with General Motors and Stellantis had not progressed significantly, but that Ford had done more to meet the union’s demands.

Mr. Biden has defended the striking autoworkers, saying when the stoppage began last week that “workers deserve a fair share of the benefits they helped create.” The White House has dispatched Julie Su, the acting secretary of labor, and Gene Sperling, a top White House economic adviser, to seek an end to the strike.

Mr. Biden has referred to himself as “the most pro-union president in American history” and has long made his alliances with and support for organized labor a central part of his political identity. But his administration’s push for a transition to electric vehicles has put him at odds with the U.A.W., because electric vehicles require fewer workers to produce.

The U.A.W. has broken with other major unions in so far declining to endorse Mr. Biden’s re-election bid.

Former President Donald J. Trump is skipping next week’s Republican presidential primary debate to instead deliver a speech in Michigan before current and former union workers. Mr. Trump pulled away significant portions of union workers from Democrats in his 2016 victory by denouncing international free trade agreements. In his current campaign, he has staked out a position against the federal push for more electric vehicles.

Senator Tim Scott of South Carolina — who, like the rest of the Republican presidential field, trails far behind Mr. Trump — sought to inject himself into the news cycle about the strike this week by suggesting that the autoworkers should be fired, a move the companies are legally prohibited from carrying out.

On Thursday, the U.A.W. postured back by filing a complaint against Mr. Scott with the National Labor Relations Board (such complaints are often dismissed). On Friday, Mr. Scott called the U.A.W. “one of the most corrupt and scandal-plagued unions in America” and said the union’s contract proposal would lead to government bailouts.

Michigan, the heart of the American automotive industry, is expected to be a key battleground state for both parties in next year’s presidential election. Mr. Trump narrowly won the state in 2016 after it backed Democrats for decades in presidential elections. Mr. Biden flipped the state back in 2020.

Democrats now control all major state offices in Michigan and have rallied to support the striking workers, with many leading elected officials appearing at rallies and on the picket lines over the last week.

Mr. Fain, who appeared at a rally with Senator Bernie Sanders of Vermont when the strike began, has been critical of Mr. Trump.