SAN FRANCISCO — In what may be the latest in a continuing spate of cyberattacks on American retailers, Michaels Stores said Saturday that it was investigating a potential security breach involving customers’ credit card information.

Michaels, an arts and crafts retailer based in Irving, Tex., said it was looking into reports of fraudulent activity on credit cards belonging to its customers. But the company said it had not yet confirmed a breach, and did not say how many credit cards were potentially compromised. The retailer operates more than 1,000 stores in the United States and Canada.

The Secret Service is investigating the breach, and is conducting separate inquiries of recent breaches at Neiman Marcus and Target.

“Although the investigation is ongoing, based on the information the company has received and in light of the widely reported criminal efforts to penetrate the data systems of U.S. retailers, Michaels believes it is appropriate to let its customers know a potential issue may have occurred,” the company said in a statement.