MEXICO CITY (Reuters) - The U.S. Trade Representative has declined to file a complaint with Mexico over alleged worker rights abuses at a Saint-Gobain glass plant, saying on Thursday that the factory's situation improved after workers elected an independent union.

The biggest U.S. labor federation last month asked the U.S. government to open a complaint, the latest in a series of petitions under the United States-Mexico-Canada Agreement (USMCA) trade pact alleging rights violations in Mexico.

A central plank of USMCA, a deal crafted at the behest of the United States, was that it would improve the lot of workers in Mexico and help stem the loss of U.S. manufacturing jobs to its lower-cost neighbor.

Major U.S. unions the AFL-CIO and United Steelworkers accused the Mexican arm of France's Saint-Gobain in the central state of Morelos of unfairly supporting its long-time union over a new, independent rival.

The office of the U.S. Trade Representative (USTR) called the allegations "troubling," but said that during its initial review, workers managed to elect the new union, the Independent Union of Free and Democratic Workers of Saint-Gobain Mexico.

Union leader Joaquin Guzman said he would have preferred the United States to follow through with the case. The union will soon begin negotiating a new collective contract, seeking higher pay.

"We'd like to think the company was acting in good faith because they knew about the possible labor complaint," Guzman said. "I hope this denial of the complaint doesn't change the company's thinking."

Saint-Gobain declined to comment.

U.S. and Mexican officials will monitor the situation, USTR said, noting that Saint-Gobain had issued a statement recognizing the new union.

"The situation at the facility improved for workers," it said in a statement. "Further immediate action on the petition is not needed at this time."

AFL-CIO International Director Cathy Feingold said the federation would check that Saint-Gobain bargains in good faith on a new contract, and urged the United States to track the matter.

Since last year, U.S. officials have raised five other complaints under USMCA.

(Reporting by Daina Beth Solomon; Editing by Bill Berkrot and Marguerita Choy)