Actor Johnny Depp has been told he has until Saturday to remove his dogs from Australia or they will be put down.
Depp and his wife Amber Heard are accused of not declaring Yorkshire Terriers Boo and Pistol to customs officials when they flew into Queensland by private jet last month.
Australia has strict animal quarantine laws to prevent importing infections.
Agriculture Minister Barnaby Joyce said he understood the dogs were being sent back to the US.
"I personally as a minister don't have Mr Depp's phone number, nor does he have mine," Mr Joyce told the BBC.
"But my department is informed they are organising for the dogs to be sent back to the United States.
"I'd say that is the wisest move."
There has been no immediate comment from Depp or Heard.
An online petition to save the "cute dogs" had received nearly 5,000 signatures by late on Thursday local time in Australia.
"Have a heart Barnaby! Don't kill these cute puppies," it appealed.
Mr Joyce said in an earlier interview: "If we start letting movie stars even though they've been the 'sexiest man alive' twice to come into our nation, then why don't we just break the laws for everybody?
"It's time that Pistol and Boo buggered off back to the United States."
The dogs' illicit entry appears to have been uncovered after a grooming salon on the Gold Coast posted pictures of them on its Facebook page.
Biosecurity officials visited the vast Gold Coast house Depp and Heard are renting on Wednesday.
"The dogs have been ordered into quarantine and the owners have been advised the dogs must be exported within 72 hours," said a statement on the agricultural ministry website.
Analysis: Wendy Frew, BBC Australia Online Editor, Sydney
There is a dog's breakfast of online stories, and commercial TV networks have sent choppers up in the hope of catching a glimpse of the Pirates of the Caribbean star and his customs-busting mutts.
Even the nation's venerable financial journal, The Australian Financial Review, has got in on the act.
Media interest in the story is so intense a mini-economy has sprouted up outside the estate with a catering van arriving to feed the press, according to the Courier Mail.
Depp is in Australia shooting the fifth film in the Pirates of the Caribbean series, Dead Men Tell No Tales.
He had flown back to the US for surgery on an injured hand in March but returned in April.
News of the threat to the star's dogs quickly spread across social media, with hundreds of Australians taking to Facebook and Twitter to express their views.
"Seriously? Not just quarantined, but being put down? I get that Depp broke a law by not telling someone about his dogs but the response is death to the dogs? That's the largest overreaction ever," said Facebook user Alexis Rogers.
"They don't have to kill the dogs. They could just quarantine them," said Bree Graham MacTaggart.
Others, however, did not express much sympathy for Depp.
"We have strict quarantine laws for a reason," said another Anne Salathiel. "He should not have brought his dogs. He can afford to do it the right way."
Can you take your dog to Australia?
- Yes, but only if it came from an approved country, is not pregnant and is not a banned breed or domestic/non-domestic hybrid
- The dog must first be fully vaccinated and microchipped before it can get an import permit
- Within 45 days of travel it has to test clear for diseases including Ehrlichia canis, Leptospirosis, rabies and parasites
- Five days before travel it must be health-checked by a government-approved vet in the export country
- On arrival it must go into government quarantine for a minimum of 10 days on arrival, longer if it is seen as coming from a riskier country or it shows signs of ill-health
- Private jets are subject to the same regulations as any other vessel or aircraft