National's police spokesperson, Chris Bishop, says deputy Police Commissioner Wally Haumaha should be stood down while complaints against him are investigated.
Two formal complaints have been laid against Mr Haumaha, accusing him of bullying.
They have been referred to the Independent Police Conduct Authority.
An inquiry is already underway into the process leading up to his appointment, led by a senior lawyer, Mary Scholtens.
The inquiry was sparked when it emerged Mr Haumaha made comments in 2004, defending police officers accused of raping Louise Nicholas in the 1990s.
National's police spokesperson, Chris Bishop, said if Prime Minister Jacinda Ardern did not stand Mr Haumaha down, he should do the right thing himself.
"Mr Haumaha will be working in an office either very near or actually within police headquarters that is near to witnesses of the alleged bullying incidents, who may be called to give evidence to the Independent Police Conduct Authority. They may also be called to give evidence to the independent inquiry."
Mr Bishop said it was normal for people who were under investigation to temporarily stand aside.