Jobs could be under threat at Swindon Borough Council as part of a new cost-cutting drive.
The 8,000 workers at the authority have been told £15m of savings must be made over the next three years.
The council is now looking at how this will be achieved and has refused to rule out job losses.
"Staff costs are an issue. I can't... say there will be no redundancies," Cllr Mike Bawden, leader of the council, told the BBC.
"It would be totally wrong of me, because I cannot guarantee it and I am not in the business - after being a councillor since 1967 - of making promises which I am not sure I can keep."
Extra responsibilities
The council wants to cut 3%, or £5m, from its budget each year for the next three years.
Cllr Bawden said the council's budget was under pressure because local authorities were being asked by the government to take on extra responsibilities.
The government has also told councils that it expects council tax bill hikes to be kept to a minimum.
Swindon Borough Council is looking at other areas of operations where savings could be made, such as procurement - the purchase of goods and services.
But councillors are determined cuts will not have an impact on public services.
A letter has been sent to all council employees informing them of the moves.
One worker said: "It's a bit concerning for everyone who works at the council.
"At the end of the day, we won't know anything until a decision is made and presumably we will be told what the outcome is as soon as possible."