Not since former prime minister Malcolm Fraser was found wandering a Memphis street without his pants in 1986 has an Australian politician so captivated the American media.

Australian Agriculture Minister Barnaby Joyce's tough talking "bugger off", directed at Hollywood superstar Johnny Depp's two tiny Yorkshire terrier fugitives from Australian quarantine, Pistol and Boo, has thrust the Member for New England into the international spotlight.

Mr Joyce's threat to kill the two illegally imported pets if Depp did not remove them from Australia by Saturday has gone global, with American reporters seemingly incredulous at the prospect.

While many Australians may have struggled to identify Mr Joyce before Thursday - and perhaps still do on Friday - he has dominated headlines, news bulletins, morning television and current affairs shows across America in the last 24 hours following his ultimatum to the Hollywood superstar.

A spokesman for the minister said he had been inundated for interview requests from across America from noted publications such as the New York Times, the Washington Post and USA Today and national television networks such as NBC and CNN.

Johnny Depp's dogs face death after being smuggled to Australia: http://t.co/AqY3IiYNnG pic.twitter.com/u6VATwhp4U— TODAY (@TODAYshow) May 14, 2015

"Captain Jack Sparrow has outsmarted Hector Barbossa, Davy Jones, Blackbeard and Lord Cutler Beckett. But he may have met his match with Agriculture Minister Barnaby Joyce of Australia," wrote New York Times scribe Rick Gladman.

The Washington Post's Adam Taylor took a more measured approach, attempting to explain to his audience the rationale behind Mr Joyce's "dramatic threat".

"It's a time-consuming, expensive and complicated process, but it serves a purpose. Australia is one of a relatively small number of countries around the world that are considered rabies-free," he wrote.

Johnny Depp's dogs face death after being smuggled to Australia: http://t.co/AqY3IiYNnG pic.twitter.com/u6VATwhp4U— TODAY (@TODAYshow) May 14, 2015

Mr Joyce's advisers were also fielding requests for interview for UK breakfast television on Friday, and he has had his own share of homegrown media appearances since the story broke Thursday morning.

Johnny Depp told his pet dogs must leave Australia or they will be put down http://t.co/euOMuGCFFr pic.twitter.com/1pDDbXu6lU— ITV News (@itvnews) May 14, 2015

On Channel Ten's The Project on Thursday night, he defended his threat to Depp earlier in the day, saying he did not hate the actor's dogs but had Australian biosecurity protection at heart.

On Friday morning, he hung up on infamous Sydney radio host Kyle Sandilands, himself no stranger to controversy, when he called the minister a "wanker".

Not to be outdone, Clive Palmer, the billionaire miner-turned-Federal-MP renowned in part for the collection of animatronic dinosaurs at his Sunshine Coast resort, the under-construction replica of the Titanic and his penchant for litigation, accused Mr Joyce of making Australia an international laughing stock.

"The simple solution would be to put the dogs into quarantine today, rather than threaten to kill them," Mr Palmer said.

"This is nothing but an embarrassing act of grandstanding by Barnaby Joyce which will result in a bad reputation for Australia and hurt the struggling film industry on the Gold Coast."

Depp is likely to face hefty fines for not declaring Pistol and Boo when he arrived by private jet at Brisbane airport last month.

He is preparing to leave the country with his wife Amber Heard and his beloved terriers on Friday night, again by private jet.

Mr Joyce's office said preparations were being made by the Department off Agriculture to enable their re-entry to the United States, after earlier fears were raised they may not be permitted back in.

"Prior to the dogs departure the Department of Agriculture will issue an export certificate and correspondence detailing the circumstances surrounding their entry into Australia to help facilitate access to the United States," the statement read.

"Given that Australia is considered to be free of rabies and that the United States has different certification requirements to us, we don't anticipate that the dogs will have any issues re-entering the United States.

"The Australian Government takes biosecurity extremely seriously.

"We have a world-leading biosecurity system that protects Australia's human, animal and plant health from exotic pests and diseases.

"It is critical that we maintain our unique pest and disease free status and we appreciate Mr Depp's cooperation in resolving this issue."