Actor Johnny Depp has told American late-night television that Australia's Deputy Prime Minister looks like he was "inbred with a tomato" in the seemingly never-ending saga over the actor's dogs.

Depp and wife Amber Heard were forced to record a video apologising for breaching Australia's biosecurity laws, after being caught illegally smuggling their dogs, Pistol and Boo, into Australia in 2015.

The then-agriculture minister Barnaby Joyce famously threatened to euthanise the dogs if they remained in the country, in one of the stranger political stories of recent years.

The case quickly gained media attention worldwide, drawing attention to Australia's strict quarantine laws, aimed at protecting the continent from overseas diseases and pests.