The elevation of Jacinda Ardern to the New Zealand prime ministership electrified pundits on social media, who predicted awkward times ahead for Foreign Minister Julie Bishop.

In the midst of the Barnaby Joyce citizenship crisis in August, Ms Bishop declared she would "find it very difficult to build trust" with New Zealand's Labour party following revelations that a Australian Labor figure made contact with a NZ Labour MP.

Ms Ardern returned fire, calling Ms Bishop's "false claims" were "highly regrettable".

"I greatly value New Zealand's relationship with the Australian government. I will not let false claims stand in the way of that relationship," she said.