(REUTERS) - Tiffany & Co on Thursday sued Costco Wholesale Corp to stop the largest United States (US) warehouse club chain from selling what it called counterfeit diamond engagement rings bearing the luxury retailer's name.

The trademark lawsuit filed in Manhattan federal court also calls on Costco to forfeit profits from the ring sales, plus damages of US$2 million (S$2.5 million) per infringement.

Tiffany said it believes hundreds, if not thousands, of Costco members bought engagement rings that they believed were authentic Tiffany products but in fact were not.

Luxury retailers often sue to stop sales of alleged imitation products that they believe cut into their own revenue streams and customer goodwill.

"This is not the kind of behavior people expect from a company like Costco, and this case will shed a much needed light on this outrageous behavior," said Jeffrey Mitchell, a lawyer for Tiffany.

Mr Mitchell also noted in the statement that Tiffany maintains an "aggressive and rigorous intellectual property program, and regularly takes actions against counterfeiters and infringers".

A spokesman for Costco was not immediately available.

In November 2012, a person who was shopping at a Costco in Huntington Beach, California complained to Tiffany that she was disappointed to see Costco offering for sale what were promoted on in-store signs as Tiffany diamond engagement rings, according to the lawsuit.

A subsequent investigation revealed that a Costco salesperson at the Huntington Beach Costco referred to rings in its display case as Tiffany rings when they were not, according to the lawsuit.

Tiffany also discovered that Costco was not using the Tiffany trademarks online for the same products at the same time to avoid detection, according to the lawsuit.