Scarborough Council has refused to budge in its stance over the mayor's civic car, despite big cuts elsewhere in its budget.
Scrapping the car would "devalue the role of the mayor", the council said.
The council is being forced to cut nearly £2.2m in the new financial year after a large dip in government funding. Scrapping the luxury car would save tens of thousands of pounds a year.
Instead, Scarborough said it would cut the cost of mayor-making ceremonies. The cost of services to the mayor came to £88,586 last year with nearly a third of it spent on the civic car and driver, the council said.
Scarborough residents said the mayor should drive himself or go to official appointments by taxi.
The mayor, John Blackburn, is driven to events in a Mercedes S600L at an estimated annual cost of £25,000.
Ian Anderson, the council's head of legal and support services, denied there were demands that the civil car service should be halted.
"Although members of the resources scrutiny committee have not recommended that the mayoral chauffeur service be discontinued, savings still need to be made and cabinet will have a difficult decision ahead of it," he said.