The 51-year-old Hollywood star and his wife, Amber Heard, are accused of breaking import laws by not declaring their Yorkshire Terriers, Boo and Pistol, to customs when they flew in to Queensland by private jet last month.
Australia has strict quarantine laws to prevent the accidental import of animal disease and infections.
Agriculture Minister Barnaby Joyce said the laws applied to everyone.
Barnaby Joyce said Boo and Pistol had been “snuck in” to Australia and were discovered when they were taken to a dog groomer.
“Mr. Depp has to either take his dogs back to California or we’re going to have to euthanise them,” he told reporters on May 14.
“He’s now got about 50 hours left to remove the dogs. He can put them on the same charter jet he flew out on and fly back out of our nation.”
Dogs brought into Australia must be law be quarantined for a minimum of 10 days after arrival, longer if they are suspected of carrying any diseases or tics.
An online petition to save the “cute dogs” had received more than 1,300 signatories by midday on May 14.
“Have a heart Barnaby! Don’t kill these cute puppies,” it appealed.
There was no immediate comment from Johnny Depp or Amber Heard.
Johnny Depp is in Australia filming the fifth film in the Pirates of the Caribbean series, Dead Men Tell No Tales.
The actor’s spokesman, Brett Chant, said the dogs were in “home quarantine”, but he did not specify where, the AP reported.
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