Hollywood star Johnny Depp has been given until Saturday to get his two pet dogs out of the country or have them put down after he brought them into Australia without declaring them to quarantine.

The Department of Agriculture is investigating after the discovery of two Yorkshire terriers – Boo and Pistol – believed to have been brought into Australia on Depp's private plane last month so their owner could resume filming on the Gold Coast for the latest Pirates of the Caribbean movie.

Sorry, this video has expired Johnny Depp's dogs given three days to leave Australia

Depp flew back to America in March for surgery on an injured hand and returned in late April.

The department said any animal that was imported without meeting Australia's import conditions would be ordered into quarantine and would either be exported or destroyed.

The department would make no comment on the individual circumstances of Depp's dogs.

The ABC understands departmental officials visited the house where Depp has been staying and delivered a three-day warning notice yesterday.

The dogs were not taken, and this morning they were spotted at the multi-million dollar mansion Depp is renting on the Gold Coast.

Johnny Depp's Yorkshire terriers Boo and Pistol at Happy Dogz groomers on the Gold Coast. ( Supplied: Happy Dogz )

Agriculture Minister Barnaby Joyce this morning said Depp had 50 hours to remove the dogs.

"There is a process if you want to bring animals: you get the permits, they go into quarantine and then you can have them," he said.

"But if we start letting movie stars — even though they've been the sexiest man alive twice — to come into our nation [and break the laws], then why don't we just break the laws for everybody?

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"It's time that Pistol and Boo buggered off back to the United States."

Mr Joyce said the dogs came to his attention after they were spotted being taken to a dog groomer on the Gold Coast.

Earlier, on ABC 612 Brisbane, Mr Joyce said "if he doesn't take Boo and Pistol back we do have to euthanase them".

"Just because he's Johnny Depp doesn't make him exempt from Australian laws," Mr Joyce said.

"The way this works is if we are going to make an excuse for Johnny Depp because he's got a private jet and brought in his dogs then I suppose you have to start making exemptions and excuses for everybody.

"The reason you can walk through a park in Brisbane and not have in the back of your mind 'what happens if a rabid dog comes out and bites me or bites my kid' is because we've kept that disease out.

"I'll tell you how close it is: it's in Bali, it's just next door. So this is not fanciful stuff, and therefore we're very diligent about what comes into our nation."

When Mr Joyce was asked if his tough stance might affect Depp's view of him, he replied: "I don't think Mr Depp will be inviting me to the grand opening of the Pirates of the Caribbean."

A US embassy spokeswoman said it encouraged US residents to do their research before travelling abroad.

"The US Department of State advises American citizens travelling to Australia that Australian customs authorities enforce very strict regulations concerning the importation from all countries of items such as agricultural and wood products, as well as very strict quarantine standards for other products, animals, and pets," the spokeswoman said.

"We advise travellers to contact the Embassy of Australia in Washington, DC, or one of Australia's consulates in the United States for specific information regarding customs requirements, and visit the Australian Government's Department of Agriculture website."

Thousands sign petition to save Depp's dogs

Within hours of Mr Joyce's comments, fans of Depp's rallied online to help save Boo and Pistol.

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Sydney woman Namita Sopal started up a change.org petition urging supporters to "Help me tell Barnaby Joyce not to kill or remove Johnny Depp's dogs from Australia".

The petition reached almost 1,000 signatures in two hours, and by 1:30pm was up to 2,300.

"It's mega. If it keeps going like it is hopefully it will create enough public attention that Barnaby Joyce will make a fair decision," Ms Sopal said.

"I just love dogs, and I saw the news this morning and thought it was crazy.

"I understand that Johnny can't just bring his dogs into the country – but the dogs shouldn't be punished."

Some of those signing the petition left messages of support for the dogs while condemning Depp and the Government.

"He should not have ignored our rules for the safety of our own dogs, but they should not be put down and pay the price for what their owner did," Carol Thompson wrote.

Linda Powell left the message: "It's not the dogs' fault. It's his stupid fault."

No special treatment for Depp

Queensland Treasurer Curtis Pitt also weighed into the debate, agreeing with Mr Joyce that Depp should not receive any special treatment because of his celebrity status.

"We have very strict laws around quarantine in this country and those should be followed; people shouldn't be getting special treatment," he said.

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"I'd hope though that if the dogs were going to be put into a situation of quarantine that he'd provide some good soft chewy toys to look at while they were in there."

Mr Pitt said he did not know if the dogs would be destroyed.

Gold Coast Mayor Tom Tate said he was a huge supporter of Depp and that Mr Joyce should had been a little more tactful with his message.

"Barnaby's right but I would put it to him this way - diplomacy is key," he said.

"I want to see Johnny Depp coming back to the Gold Coast, enjoy his experience here ... so that he'll have good words to say and make sure our film and television industry thrives here."

'This is a serious matter'

One of Depp's dogs being groomed on the Gold Coast. ( Supplied: Happy Dogz )

Meanwhile, Immigration Minister Peter Dutton said Depp could face large fines for breaching quarantine procedures.

Speaking on Macquarie Radio, Mr Dutton said it was a serious matter "because if you have breaches of biosecurity, it can have big impacts".

"That's why people can't bring plants or animals in, they need to notify Customs and the AQIS people at the borders, and we need to make sure that they're not bringing in diseases," he said.

"In this case it should have been screened, it wasn't, and [Mr Joyce] is obviously having a good look at it.

"As people know when they come in on a commercial flight ... you need to make declarations and so people will sometimes make false declarations, if they get caught out, there's a big fine attached to it, and no different to the same cards that people would need to fill out if they're coming in on private jets."

"But there should have still been a proper screening process that took place."