Councillors in Stocksbridge say traffic congestion in the Leppings Lane area has been made worse by lights changing to red - causing problems from the town travelling to and from Sheffield to work.
They say their colleagues at Sheffield Town Hall claimed traffic lights weren't changed to red to give priority to Supertram. But Mayor Coun Alison Brelsford insisted Supertram did have priority at traffic lights.
The mayor said: "Every time a Supertram approaches traffic lights they automatically turn to red to stop other traffic and then tram goes through."
Coun Mary Kaye said traffic lights frequently changed to red to let Supertram pass and traffic congestion in Hillsborough was now a very serious problem.
Coun Matt Davis said: "Whatever the city council may say there is no doubt that Supertram is responsible for massive hold ups for other traffic because of the traffic light priority system for Supertram."
But a Sheffield Council spokeswoman denied the council had ever said Supertram did not have priority at the junction. "It would seem that Stocksbridge Town Council has made some sort of misinterpretation of our letter if it believes this to be the case," she said.
"The trams do have priority at Hillsborough and at all signal controlled junctions in Sheffield on the tram route. This allows trams to negotiate junctions in a safe and efficient manner and to minimise the overall disruption to other road users."