A dozen trade groups are joining the call for Chinese e-commerce giant Alibaba Group Holding Ltd. to be put back on a list of global marketplaces known for counterfeit and pirated goods.

In a letter to the U.S. Trade Representative Wednesday, these trade groups—including the Federation of the Swiss Watch Industry, the Council of Fashion Designers of America and the Travel Goods Association—said they were making the request because an “enormous amount of counterfeits” remain on Alibaba’s sites, especially its flea-market-like...