Ms Dalziel rejected this.
"I asked myself before I put my hand up whether I would run for the mayoralty if I'd been promoted to the front bench. My answer was yes," she said.
"I believe that the city needs me to run and I'm prepared to deliver the sort of leadership that the city's looking for."
Ms Dalziel was adamant that she wanted to run a non-party campaign, which was indicated when she asked Student Volunteer Army founder and National Party member Sam Johnson to be her running mate, an offer he ultimately turned down.
Mr Parker said she was "daydreaming" if she thought she could sever her Labour Party ties.
"The reality is the group that are backing her are the Labour Party group in Christchurch. It is smoke and mirrors, frankly," he said.
He also sullied Ms Dalziel's assertion that her experience working with central government made her right for the job, given her shaky relationship with Earthquake Recovery Minister Gerry Brownlee.
"I haven't called for Gerry Brownlee to resign, I haven't had face-to-face battles with him in Parliament," Mr Parker said.
"I just think there's a dent in her credibility when she says she's going to have a wonderful relationship with Gerry because her history just does not show that."
Mr Parker has had his own well-publicised arm-wrestle with Mr Brownlee over the time Christchurch City Council takes to grant consents, but he said their relationship was "happily robust".
An online poll by Christchurch newspaper the Press this afternoon had support for Mr Parker at 47.1 per cent and Ms Dalziel at 40.8 per cent, with 12.1 per cent supporting neither.
Despite this slim margin, Mr Parker was confident he would win.
"I think I'm very well placed to take us through the next three years - a crucial three years for Christchurch - and I think some people will be asking whether it's the right place for a Labour Party politician when you've got a National Party Government."
Ms Dalziel said she would resign as MP for Christchurch East before the local government election, which she said showed she was "all-in" for the mayoralty.
This will spark an expensive by-election - The Electoral Commission said they generally cost about $600,000 - which Ms Dalziel said had made deciding to run a tough decision.
"I had to ask myself what the price democracy is. But the alternative was for me to stay on as the MP beyond the mayoral campaign and I'm not prepared to do that. I think people have a right to know that I'm all in for the mayoralty and I'm not going to have a fall-back position."