He told Radio New Zealand he would still be going on the trip - despite calls for him to remain in the city to sort out the council's issues.
"We're not going to let down the many, many events that have been organised for us," he said.
"I think these events have been built around my presence, and I'm very happy that we are making good progress in the city. I've spoken to the minister, I've spoken to the Crown observer and I've asked the councillors and I've been given their blessing.
"So I think that it is appropriate that I honour engagements and commitments we've made on behalf of the city."
Mr Parker said calls for progress to be made to amend the council's issues over the next few weeks are unrealistic.
"I'm dealing with the real world. I've got work to do, a city to rebuild and a council to pull together and that's where our focus is."
Mr Parker said he has spent a lot of time already this week working with the Crown observer and will be meeting again later this month and in March.
"I'm very certain that my council has the ability to pull together, if it chooses to pull together, and do a great job for its city."
Many at yesterday's protest were pledging to stop paying rates in protest.
"There is a process around paying rates, it's controlled by laws, not just my council, and they would have to confront that as well," Mr Parker told Radio New Zealand.