The Hollywood star and actress-model Amber Heard released the video after she admitted failing to declare their dogs Pistol and Boo when they flew in to Queensland a year ago.
In it, Heard says: “Australia is a wonderful island with a treasure trove of unique plants, animals and people.
“It has to be protected.”
Depp then deadpans that Aussies are “just as unique” as their wildlife.
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The video – which has received more than two million hits on YouTube – has been compared with a hostage plea or North Korean-style propaganda on social media.
Barnaby Joyce, who is also the country’s agriculture minister, last year threatened to have the couple’s pet dogs put down unless they “b***ered off back to the United States”.
And on Tuesday he could not resist a dig at Depp.
“I don’t think he’ll get an Academy Award for his performance … he looked like he was auditioning for the Godfather,” Mr Joyce told the Australian Broadcasting Corporation.
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He went on: “At the end of it we’ve got a message that is going all around the world right now.
“It’s going off like a frog in a sock telling people that if you come into this nation and you don’t obey our laws, you’re in trouble.
“That’s what this is about, it’s making sure we keep this nation, protect our flora, our fauna and protect our biosecurity laws.”
Australia has strict quarantine laws to prevent pests and diseases entering the country.
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