The U.S. Food and Drug Administration says that samples of pasteurized milk have tested positive for remnants of the bird flu virus that has infected dairy cows.

The agency stressed that the material is inactivated and that the findings "do not represent actual virus that may be a risk to consumers." Officials added that they're continuing to study the issue.

"To date, we have seen nothing that would change our assessment that the commercial milk supply is safe," the FDA said in a statement on Tuesday.

The announcement comes nearly a month after an avian influenza virus that has sickened millions of wild and commercial birds in recent years was detected in dairy cows in at least eight states. The Agriculture Department (USDA) says 33 herds have been affected to date.