WASHINGTON, June 21 (Reuters) - The Biden administration said on Monday it was working closely with the United Autoworkers union in pressing Mexico to probe alleged labor rights violations at a General Motors Co (GM.N) plant in that country, and vowed to fight for a worker-focused trade policy. U.S. Trade Representative Katherine Tai told members of the UAW union during a visit to Flint, Michigan, that the Biden administration would work to implement trade policies that lifted wages and expanded opportunity for workers everywhere. "At USTR we want to encourage a race to the top with higher standards and real, rapid enforcement of our trade agreements," she said. "We don’t want to create incentives for companies to move jobs overseas to maximize profits." Tai told the autoworkers the U.S. government"s decision to initiate a case against the GM facility reflected the Biden administration"s determination to fully enforce labor standards negotiated under the U.S.-Mexico-Canada trade agreement. "We know that protection unions in Mexico don’t actually represent the workers. When workers are denied independent union representation, it is easier to suppress wages," she said. The case, the first brought under the Rapid Response Labor Mechanism in USMCA, could lead to tariffs on some of GM"s most profitable vehicles under the North American trade deal. read more Tai, the former top trade lawyer on the House Ways and Means Committee, helped negotiate the labor enforcement mechanism on behalf of Democrats in the U.S. Congress. Tai and Democratic U.S. Representative Dan Kildee met with workers at UAW Local 598 in Flint, before touring a mobile COVID-19 vaccination site and encouraging people to get vaccinated.