Fairfax County police officers have been banned from wearing the American flag and other patches on their outer ballistic vests, a move that has angered some of the rank and file who say the policy is unpatriotic.

Major Cindy McAlister and other top brass announced the change in an e-mail to patrol bureau commanders late last month, writing that officers should be wearing only a cloth name tag on vests.

“It’s been brought to our attention that some officers are not wearing their name on their exterior cover, in addition, some are placing unapproved patches on the Velcro, such as the American flag,” McAlister and other top officials wrote in an e-mail obtained by The Washington Post.

The move prompted an outpouring of anger from officers, said Joseph Woloszyn, president of the Virginia Police Benevolent Association. He said he has fielded more than 30 calls on the issue, and that some officers have told him they will defy the directive even if it means punishment.

He said he did not see a good reason for the department to ban American flag patches and those that say “police” on them.

“It’s a matter of identification with the police patches,” Woloszyn said. “Banning American flag patches is just un- ­American.”

Lucy Caldwell, a police spokeswoman, said the intent of the directive was to create uniformity in what officers are displaying on their vests, since there are no rules on such displays.

She said the department is creating guidelines for what can be displayed.

“It’s a temporary thing,” Caldwell said of the policy. “An American flag will likely be welcome on the final model of outer vests that are selected. The flag is approved and used widely on our uniforms.”

Caldwell said the department has approved a flag pin and patch for use on different parts of the uniform.