Johnny Depp has addressed the apology video he made to Australia with his wife Amber Heard last month, for failing to put their dogs through proper quarantine procedures.

In April, Amber Heard received a AUS$1,000 (€679) good behaviour bond with no conviction after pleading guilty to providing a false immigration document which failed to declare her dogs.

The case was dubbed the "war on terrier" and began in May 2015 when Agriculture Minister Barnaby Joyce accused Depp of sneaking the terriers aboard his private jet when he returned to Australia for the filming of Pirates of the Caribbean: Dead Men Tell No Tales.

Australia has strict quarantine regulations to prevent diseases such as rabies from spreading to its shores. Bringing pets into the country involves applying for a permit and quarantine on arrival of at least 10 days.

Depp and Heard were given 72 hours to send Pistol and Boo back to the US, with officials warning that the dogs would otherwise be euthanised. The pooches boarded a flight home just hours before the deadline ran out.

The couple recorded a public apology for the Australian Government Department of Agriculture and Water Resources that was played out in court, where they "awkwardly" spoke about the importance of Australia's biosecurity laws.

Speaking at a press event today for his new movie Alice Through the Looking Glass, Depp poked fun at the apology video he recorded with his wife: "I would really like to apologise for not smuggling my dogs into England".