By Robin Sidel 

American Express Co. is keeping its cards close to its vest.

The company's top executives steered clear of telling investors how they plan to make up for any disappearing revenue that could result from losing Costco Wholesale Corp. customers after AmEx's 16-year exclusive partnership with the warehouse club ends next year. The Costco deal affects one in 10 AmEx cards in circulation.

"Our intent is to provide these customers with high-value proprietary products that meet their spending needs," said Kenneth Chenault during an investor meeting that lasted nearly four hours. Neither he nor AmEx President Ed Gilligan provided details about those plans at Wednesday's meeting.

The loss of Costco is one of a number of challenges facing AmEx, which also last month lost a big antitrust case. The company is also falling short of its revenue goals.

Mr. Chenault said the company plans to seek a stay of a judge's recent ruling in the antitrust case, a ruling that could permit merchants to steer consumers to cheaper cards from Visa Inc. and MasterCard Inc.

He defended the company's decision to fight the lawsuit filed by the Justice Department in 2010 that led to the judge's ruling last month. The federal judge determined AmEx's rules for merchants violate antitrust laws.

"Fighting this suit was the right call in 2010, and continuing to fight is the right call now," Mr. Chenault said.

AmEx, which has said it would appeal the ruling, will begin that process after the judge sets a remedy in the case, Mr. Chenault said. Although the judge sided with the government in the case, he didn't lay out a remedy at the time of the ruling. Both sides filed their proposals for a remedy earlier this week.

Mr. Chenault added that AmEx intends to compete aggressively on other co-branded partnerships that are expected to come up for renewal in the next 18 months. It isn't clear, however, whether any new partnerships would provide AmEx with the exclusive acceptance it now has with Costco.

Some 70% of spending on AmEx's co-branded Costco cards takes place outside the warehouse stores, meaning AmEx will be under pressure to shift those cardholders to its other products when the relationship ends.

Shares of AmEx fell $1.26, or 1.6%, to $80.11 on the New York Stock Exchange.

Write to Robin Sidel at robin.sidel@wsj.com

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