During an appearance on "Jimmy Kimmel Live!," Depp was asked about an infamous video he filmed with wife Amber Heard
apologizing for illegally bringing their dogs into Australia.
Depp joked about the video and said that Joyce -- who, as Australia's agriculture minister, had threatened to euthanize the Yorkshire terriers unless they were removed from the country
-- "looks somehow, like, inbred with a tomato."
"It's not a criticism. I was a little worried," he said, referring to the minister as "Barnaby Jones."
Joyce: I'm his Hannibal Lecter
Joyce, who has been embroiled in a public feud with the actor since the dogs were brought into Australia on a private jet in April last year, took the insult in stride at a news conference Wednesday.
"I think I'm turning into Johnny Depp's Hannibal Lecter, aren't I?" he said, Australia's public broadcaster ABC reported.
"I'm inside his head, I'm pulling little strings and pulling little levers. Long after I've forgotten about Mr. Depp, he's remembering me."
Last month, Joyce mocked Depp's stilted performance in the apology video
, saying he "looked like he was auditioning for the Godfather" and urging him to re-shoot it with "a little gusto."
Depp: I didn't watch video
Depp disparaged the apology during his conversation with Kimmel, telling the talk show host he hadn't watched it before releasing it, "because I didn't want to kill myself."
He also joked about the notion that the dogs, Pistol and Boo, were "a problem" in Australia, a country he said had "so many poisonous creatures... you could die at any minute."
It was not the first time he had joked about the video
since the incident, which occurred when he flew to Australia to film a "Pirates of the Caribbean" movie.
Heard was spared a conviction over the incident and given a one-month good behavior bond sentence instead.
Joyce said at the time that he was pleased the video was spreading an understanding of Australia's biosecurity laws to an international audience.
"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," he told ABC.