Joe the pigeon is on death row, with federal quarantine officials threatening to kill the bird over fears it could spread disease.
Michael McCormack was not aware of Joe's plight - or flight - but indicated there was little room for compassion on biosecurity laws.
"If Joe has come in a way that has not met our strict biosecurity measures, then bad luck Joe," the acting prime minister said.
Either fly home or face the consequences.
The Nationals leader's take-no-prisoners stance aligns with predecessor Barnaby Joyce, who infamously threatened to have two Yorkshire terriers euthanised in 2015.
Mr Joyce warned Hollywood stars Johnny Depp and Amber Heard their dogs Pistol and Boo would die unless they "buggered off back to the United States" after dodging quarantine requirements.
An emaciated Joe the pigeon arrived in Kevin Celli-Bird's backyard on Boxing Day, crossing the Pacific after being reported missing from a race in the US state of Oregon on October 29.
The bird is named after US president-elect Joe Biden and is believed to have hitched a ride on a ship after being blown off course.
Mr Celli-Bird plans to contact Joe's owner after receiving his details through American pigeon racing authorities.
"He certainly should have turned left at Albuquerque," Mr Celli-Bird told the Seven Network.
Victorian Animal Justice Party MP Andy Meddick wants the federal government to put the bird in quarantine rather than kill it.
"Should the federal government allow Joe to live, I am happy to seek assurances that he is not a flight risk," he said.
My message to the federal government is this: take Joe off death row.
Victorian Health Minister Martin Foley is also in the "save Joe" camp.
"I would urge the Commonwealth quarantine officials to show a little bit of compassion to Joe," he said.
The minister was asked whether the state government was showing compassion to Victorians stranded in NSW because of border closures.
"I'm pretty sure we're not planning to euthanise the people from Victoria who are in New South Wales, so I will take great exception to that," Mr Foley said.
The agriculture department said the pigeon was not permitted to remain in the country because it could compromise Australia's food security and wild bird populations.
"It poses a direct biosecurity risk to Australian bird life and our poultry industry," it said in a statement.