Philip Allott, the Police, Fire and Crime Commissioner (PFCC) for York and North Yorkshire, said on Friday that Ms Everard should not have submitted to her arrest by serving Met Police Officer Wayne Couzens.
Couzens was sentenced to life in prison last week after kidnapping Ms Everard, 33, on her walk home in Clapham before raping and murdering her.
Mr Allott, who was elected last year, told BBC Radio York: “Women, first of all, need to be streetwise about when they can be arrested and when they can’t be arrested. She should never have been arrested and submitted to that.
“Perhaps women need to consider in terms of the legal process, to just learn a bit about that legal process.”
Mr Allott later apologised for the comments.
But the remarks sparked calls for his resignation led by Labour leader Sir Keir Starmer and backed by the Bishop of Ripon, Helen-Ann Hartley.
Yesterday the leader of North Yorkshire County Council, Carl Les, who chairs the region’s Police and Crime Panel, said Mr Allott will have to explain himself before the panel, which meets later this month.
Carl Les said: “The panel members will want to have their say. The purpose of the panel is to hold the Commissioner to account, so it would be very remissive of us if we didn’t hold to account the remarks he said in the press.
“It’s also incumbent on us to give him an opportunity to explain himself.”
Serious complaints against Commissioners are handed by Police and Crime Panels to the Independent Office for Police Conduct, which will only investigate if there is an allegation of criminal behaviour.
There is no legislation to remove an elected PFCC, although it was discussed by MPs in 2014.
A petition calling for Mr Allott’s resignation, started by York woman Justine Hughes, has received almost 5,000 signatures.
But Mr Allott said yesterday that he would not be resigning, and asked the public to accept his apology, admitting his remarks were “misconceived and insensitive.”
He said: “Clearly, I have much to learn, so as well as committing to working ever more closely with subject-matter expert colleagues in my own organisation and beyond, I will be seeking meetings as soon as possible with local partner organisations that provide services to tackle male violence against women and girls, in order to deliver on their concerns and broaden my understanding of the issues.”
Senior Labour MP Yvette Cooper joined the criticism of Philip Allott after his remarks.
She said: “Phillip Allott’s comments were disgraceful and out of touch. The responsibility of Police and Crime Commissioners is to make sure police forces do their job keeping women safe and rebuilding trust - not to lecture women with highly unrealistic accounts of what we should have to do in order to stay safe.”
Yesterday Conservative party chairman Oliver Dowden said the remarks were “stupid” but would not be drawn on whether Mr Allott would be deselected by the party for the next PFCC elections.
Mr Dowden said Boris Johnson had been “outraged” by the comments.