Costco Wholesale Corp should hand over $5.5 million to compensate Tiffany & Co for selling counterfeit Tiffany diamond engagement rings, a federal jury said on Thursday.

Tiffany is also entitled to punitive damages, the jury in Manhattan said. Lawyers for both sides were presenting evidence on Friday to help determine the amount of punitive damages.

The trial, which began on Sept. 20, was aimed at determining the amount in total damages that Costco is liable for, after U.S. District Judge Laura Taylor Swain ruled last year that Costco had willfully infringed Tiffany's trademark by selling rings bearing the luxury retailer's name.

Tiffany spokesman Nathan Strauss declined to comment on Friday. In a statement on its website, Costco said it would not comment because jury deliberations were continuing.

The $5.5 million represents the amount of profit Costco made from the sale of the rings that would fairly compensate Tiffany, said the jury, which was made up of five men and two women.

The amount far exceeds the $781,000 that Costco had argued at the start of the trial was the maximum it owed. Costco said about 2,500 rings it sold were found by the court to have infringed Tiffany's trademark.

A model poses backstage ahead of a Tiffany and Co. show. Lisa Maree Williams/Getty Images for Audi Fashion Festival

Costco had also argued that Tiffany's trademarks were invalid because they sought to prevent others from using the word "Tiffany" as a generic description of a type of ring setting.

But Swain rejected that argument and said Costco confused consumers by using the word Tiffany in display case signs.

She said Costco's jewelry buyers had asked vendors to copy Tiffany designs, and that evidence showed Costco employees were aware of customer confusion but did nothing to remedy it.

The case is Tiffany & Company and Tiffany (NJ) LLC v. Costco Wholesale Corp, U.S. District Court, Southern District of New York, 13-1041.