Brown said his earlier comments were in response to a hypothetical question and had been blown out of proportion.
But his Auckland mayoral rival Kerrin Leoni accused him of not being fully committed.
Auckland mayoral candidate Kerrin Leoni has criticised what she views as Wayne Brown's campaign tactics. Photo / RNZ, Jessica Hopkins
“Why would you put your name up to be mayor if you’re talking about possibly finishing the job halfway through the term and handing it over to someone else? That’s really poor leadership.”
She speculated his comments were a campaign strategy.
“Voter turnout is low. I’m sure he and his campaign team are concerned whether they had to pull a comment out like that because the feedback I’m hearing – even from people who would normally be voters from the right – is that they’re not confident about his leadership.
“Saying something like Desley taking over, I think, is just a tactic to try and get more votes.”
Less than two weeks out from a new mayor being elected, almost 12% of eligible Aucklanders had cast their votes.
Brown previously confirmed Simpson would remain as deputy mayor if he was re-elected on October 11.
Auckland Mayor Wayne Brown is seeking a second term in office. Photo / RNZ, Marika Khabazi
She is standing for re-election as the Ōrākei Ward councillor unopposed on Brown’s Fix Auckland ticket.
Leoni said Simpson was also her first choice to be her deputy if she was elected.
“I would be more than happy to have her as my deputy mayor and to work with her to run the city.”
A spokesperson for Brown’s campaign said Leoni’s suggestion was laughable.
“Wayne and Desley have been on a united ticket for this election. People have been impressed by having a strong team approach, united in wanting to fix Auckland.”
Simpson said she was not expecting to replace Brown if he was re-elected.
“As I have said many times, I am very happy to support Wayne as we deliver for Auckland through the next term. My understanding is that he was talking about a purely hypothetical scenario as it’s not something we’ve discussed.”