The audio recording of Simon Bridges and Jami-Lee Ross contains the National leader calling one of his MPs "f*****g useless".
In the recording, made earlier this year, the pair discuss a party donation, the race of some list MPs, and which MPs should be pushed out.
When Mr Bridges mentions the National list, he said he was not talking about "obvious ones like Finlayson or Carter" but said there were some "we just want them to go, like Maureen Pugh is f*****g useless".
In the recording, Jami-Lee Ross says, "Carter, Finlayson, Nicky Wagner, they don't really need to hang around".
"Yeah, but we don’t want them to go this year though," Mr Bridges says.
Simon Bridges quickly apologised for the comments about Ms Pugh.
He said on Twitter: "I have just met with @MaureenPughNat and unreservedly apologised for my comment. It was inappropriate. I value the work she does as the National List MP based in West Coast-Tasman & as our Associate Spokesperson for Children. She has gracefully accepted."
Ms Pugh, the National candidate for West Coast-Tasman, re-entered Parliament after Sir Bill English resigned. She previously came into Parliament after Tim Groser left in 2015, after winning a seat in 2014, but losing it when special votes were counted.