The fallout from the massive data breach announced by insurer Anthem Inc. earlier this week just got larger. The company behind Blue Cross Blue Shield insurance informed customers Friday to be wary of an email scam that is aimed at current and former Anthem members.

The email is designed to look as if it comes from Anthem and asks customers to click on a link for credit monitoring in the wake of the hack that affected up to 80 million records. In a statement, the company says emphatically that the emails are not from Anthem and tells customers to:

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Not reply to the emails.

Not supply any information on the website, if you clicked on it.

Not open any attachments that come with the email.

Anthem said it is not calling members about the hack and is not asking for credit card information or social security numbers over the phone.

"Anthem will contact current and former members via mail delivered by the U.S. Postal Service about the cyber attack with specific information on how to enroll in credit monitoring. Affected members will receive free credit monitoring and ID protection services," the statement said. Criminals can use some of the information stolen in the data breach, such as social security numbers and medical numbers, in medical ID fraud and tax ID fraud.

IN-DEPTH

-- Patrick Rizzo and Matthew DeLuca, NBC News