"If you start letting movie stars - even though they've been the sexiest man alive twice - to come into our nation (with pets), then why don't we just break laws for everybody?" Joyce said. "It's time that Pistol and Boo buggered off back to the United States."
The doggie drama prompted a petition to save the pooches and the social media hashtag #WarOnTerrier. Joyce received both commendation and criticism, with some praising him for defending Australia's laws and others cringing over a perceived crass response.
A spokeswoman for the Agriculture Department who spoke on customary condition of anonymity said Depp's case is a rarity, with only an average of one dog per year arriving in Australia without the proper permit. The choice given to Depp is in line with policy: either returning the animal to its home country, or having it euthanized.
Other animals have proved problematic in the past.
"We've had other dignitaries who've brought in, for instance, bullfrogs...to eat. We had to euthanize them," Joyce told the Australian Broadcasting Corp.
During an interview, radio shock jock Kyle Sandilands said the minister had invited the wrath of all dog lovers and had made Australians sound like "a bunch of hillbilly redneck losers." Joyce, undeterred, responded that the law was the law. Sandilands then unleashed a torrent of insults at Joyce - calling him a clown and a disgrace - before the minister retorted: "You're a savage little man, aren't you?" The interview promptly ended.
The department learned of the dogs after they were taken to a dog groomer, Joyce said. How the pets entered through Brisbane Airport without an import permit is being investigated.
Depp's publicist has not responded to requests for comment.
The filming of Pirates of the Caribbean: Dead Men Tell No Tales was disrupted in March when Depp, who plays the pirate captain Jack Sparrow, cut his hand on a glass door. He underwent surgery in the US.
- AAP