WASHINGTON (Reuters) -Workers at Volkswagen's Chattanooga, Tennessee, assembly plant are seeking an election to join the United Auto Workers union, setting up a critical test for UAW President Shawn Fain's unprecedented campaign to expand the union's reach to foreign-owned automakers in the southern United States.

The UAW said a supermajority of eligible workers at the VW plant have signed union cards in about three months. The workers have filed a petition with the National Labor Relations Board (NLRB) seeking a vote to join the union. It would be the third time in 10 years that the UAW has sought to represent VW Chattanooga workers.

For more than two decades, the UAW has tried and failed to organize non-union U.S. auto assembly plants established by Asian and European automakers, mostly in southern states with laws and political leaders that are hostile to unions. The UAW has not organized workers at Tesla or other electric vehicle startups such as Rivian.

Winning a vote to organize the VW plant would be a significant milestone for the UAW in an election year where both U.S. President Joe Biden and his presumptive Republican rival Donald Trump are aggressively courting votes from UAW members in Michigan and other industrial swing states.

Biden, in a statement released by the White House, congratulated the workers and noted that many VW plants internationally were unionized. "As the most pro-union president in American history, I believe American workers, too, should have a voice at work. The decision whether to join a union belongs to the workers," Biden said.

After winning record new contracts with the Detroit Three automakers last fall, Fain launched a first-of-its-kind campaign to organize the entire nonunion auto assembly sector in the U.S., initiating simultaneous organizing efforts at non-union operations owned by Toyota, Mercedes, Hyundai and other automakers.

VW, which produces the Atlas and ID.4 at the plant, said Monday it "will fully support an NLRB vote so every team member has a chance to vote in privacy in this important decision. The election timeline will be determined by the NLRB."

The NLRB said it had received the union election petition for 4,300 employees at the VW plant to be represented by the UAW. If both sides do not agree on the election details, the NLRB will hold a pre-election hearing on March 26 in Atlanta.

Two attempts to organize VW's plant in Chattanooga narrowly failed. In 2019, VW workers at the plant rejected union representation in an 833-776 vote. Earlier efforts to organize Nissan Motor plants in Mississippi and Tennessee also failed by wide margins.

The UAW in November announced campaigns at 13 nonunion automakers, including at Tesla, Toyota Motor, Hyundai, Rivian, BMW and Mercedes-Benz. Senators in January pressed the automakers to remain neutral during organizing.

Earlier this month, the UAW said that more than 30% of workers at a Toyota factory in Missouri are seeking to join the union.

The UAW said last month a majority of hourly workers at a Mercedes Benz Alabama factory have signed union authorization cards.

VW said in November it would hike pay for Tennessee factory workers by 11%, joining several foreign automakers who have announced significant pay and other compensation improvements in response to the UAW contract.