On Tuesday, Bishop held a press conference to say she would find it difficult to work with a New Zealand Labour government if the party had any role in uncovering Barnaby Joyce's dual citizenship. NZ Labour leader Jacinda Ardern has called the claims "false" and "highly regrettable".

In the wake of the diplomatic row, The Project NZ's Jesse Mulligan took to national TV to mock Australia and New Zealand's "so-called special relationship". He said Bishop's comments sound like a "serious threat" but, in reality, Australia has been treating New Zealanders like "dirt" for several years.

"Despite these longstanding agreements which are supposed to give us special rights, New Zealanders seeking a better life in Australia have not been made to feel welcome," he said.

Mulligan pointed out New Zealanders living in Australia are not able to access unemployment benefits, university subsidies or disaster relief. He also accused the Australian government of having "betrayed" a promise to give New Zealanders quicker access to citizenship.

"When Aussies arrive in NZ they get the full ANZAC treatment," he said. "Permanent residency ... access to student loans and benefits. Becoming a citizen costs less than $500."

The TV host said New Zealanders arriving in Australia "get none of that".

"When our politicians raise it in meetings we get ignored," he said. "The 600,000 Kiwis in Australia can't do anything about it because despite paying full taxes they're not allowed to vote.

"In 2017, Australia is basically a bully. So, Julie Bishop, when you say you'll find it hard to work with New Zealand - what exactly do you mean? How much worse could it possibly get?"