Councillors Vaughan Dennison, Billy Meehan and Karen Naylor said they would support the mayor's motion.
Smith said the extra parking-fee revenue the council expected to receive had been built into its 10-year-plan finances, but the council should go in good faith and talk to the community.
The notice of motion means council officers cannot act on the matter until it is considered at the June 30 meeting.
Chief customer officer Chris Dyhrberg said he was in the middle of recruiting more parking wardens.
Keating said from July 1 paid parking hours would increase from 49 to 70 and a half hours.
He said most events in Palmerston North were on Thursday to Sunday, usually in the evenings. The new paid hours would be a barrier to people attending these events and affect the city's vibrancy.
"Go out and talk to businesses and stakeholders, talk to people at the coalface. Get their thoughts and opinions."
At the June 16 economic development committee meeting, Manawatū Chamber of Commerce chief executive Amanda Lindsay and chairman Rob Campbell expressed their concerns about the changed hours and the effect this would have on businesses, staff and shoppers in the city centre.