The local authority said the average call took around eight-and-a-half minutes to be answered last month and that it was committed to bringing waiting times down even further.
It follows comments by local Labour councillor John Illingworth, who said he was aware of people who’d spent “an hour-and-a-half” trying to get through to the council.
He also criticised a “misleading” automated message which he said greets callers and tells them they will speak to a human shortly.
The council said it disagreed with that characterisation and claimed that while some people may have to wait a long time during busy hours, such instances were “not reflective of the overall situation”.
Speaking at a meeting of the council’s audit committee on Friday, Coun Illingworth said: “This is not a Leeds City Council-specific problem. It’s a problem for all large, corporate organisations.
“But if you call up, the spiel says, ‘we’re currently experiencing high call volumes and there may be a delay before your call is answered. Please stay on the line and we’ll do our best to assist you’.
“You can be stuck there for an hour-and-a-half on the back of that message, told to hang on, but with no hope of getting an answer from the system.”
Councillor Illingworth, who represents the city’s Kirkstall ward, said that the system was not working and “misleading” residents.
He explained: “If the message was, ‘we have a monstrous queue and no-one’s answering questions,’ at least people could go away and call some other time.
“It’s when you’re encouraged to stay and there’s no hope of a response (that there’s a problem).
“I’ve had two complaints already today about this practice.”
Coun Illingworth’s comments came following remarks made by Conservative councillor Sam Firth, who represents the city’s Kirkstall ward, and had previously raised the issue of long waiting times at a meeting earlier last week.
Speaking on the issue Coun Firth said he believed the problem was, “Largely due to the fact people can’t access services online”.
A spokesperson for Leeds City Council said: “We are committed to ensuring that the process for residents contacting the council is quick and easy and therefore provide multiple methods of contact, including by telephone.
“The average time for calls to be answered during July 2022 was 511 seconds and over 60 per cent of calls were answered with five minutes.
“Individual extended waiting times may occur on specific query lines at busy times of the week, however these are not reflective of the overall situation.”
The council said it used recorded messages to help keep people informed of waiting times but said it did “not accept that they are misleading”.
They added: “We are not, however, complacent, and there is an ongoing programme of improvement work taking place that is bringing down call waiting times and offering better online options for customers.”