Councillor Gordon Edgar has said the lack of traffic wardens has led to “chaos on Selkirk High Street”.
Mr Edgar, chairman of the council’s environment and infrastructure committee, made the comment at a meeting last week.
He added: “Buses cannot get past and I would hate to see what would happen if a fire engine needed to get past.
“People are parking on both sides of the road and it is causing a great deal of concern.”
At last Thursday’s meeting of the committee, Hawick councillor Ron Smith said the postponement of the removal of the police-run traffic warden service until the end of April was an “empty gesture”.
Mr Smith added: “To say it will continue to the end of April is meaningless when two of the three wardens in the Borders have stepped down already.”
Mr Edgar also warned: “Although Police Scotland are having to save money, SBC are having to save money too, and if it is going to cost us to provide this service we will have to cut another service to do it.”
Councillor Edgar, along with councillors Smith, Cockburn and Logan, agreed to join a working group along with council officers to try to find a solution in relation to on-street parking enforcement when the service does end.