(CNN) -- The U.S. Food and Drug Administration has a message for veterinarians and pet owners: If dogs or cats get sick after eating jerky pet treats, let us know.

The agency says it's received reports of more than 3,600 dogs and 10 cats that got sick after eating jerky pet treats since 2007. Of those cases, the FDA says, more than 580 pets have died.

"This is one of the most elusive and mysterious outbreaks we've encountered," said Bernadette Dunham, director of the FDA's Center for Veterinary Medicine.

"Most of the jerky treats implicated have been made in China," the FDA said. Investigators have tested more than 1,200 samples but haven't uncovered what could be causing the illnesses.

On Tuesday, the FDA issued a letter to veterinarians asking for help tracking the illnesses. The agency also released a fact sheet for pet owners warning of possible symptoms, including decreased appetite, decreased activity, vomiting, diarrhea, increased water consumption and increased urination.

"FDA recommends that pet owners whose pet becomes sick after eating jerky pet treats should hold on to any unused portion of the product in its original container for at least 60 days, in case FDA calls to request samples for testing," the fact sheet says. "Owners should place the container inside a sealable plastic bag, if possible."

The FDA says there isn't a particular brand for which consumers should watch.

"The illnesses have been linked to many brands of jerky treats," the FDA says. "The one common factor the cases share is consumption of a chicken or duck jerky treat or jerky-wrapped treat, mostly imported from China."