The deputy city mayor has criticised a private transport company responsible of ferrying people two and from hospital of letting patients down.
Councillor Rory Palmer, who is also chairman of Leicester City Council's health and well being board, was speaking out after it emerged that Arriva Transport Solutions had failed three out of five standards following a recent inspection by the Care Quality Commission.
Leicester West MP and shadow health Minister Liz Kendall has also called for improvements.
The company has come under fire after two women in their late 80s had to wait more than 10 hours for a lift home from Leicester Royal Infirmary.
Coun Palmer said: "Too many patients are receiving an extremely poor service from Arriva Transport Solutions.
"This poor performance is unacceptable and urgent improvements are needed.
"There are consequences across the health and care system in the area because of this poor performance.
"This is yet another example of big, national companies winning lucrative NHS contract up and down the country and letting patients down."
He added: "My view is that Arriva Transport Solutions should be given a maximum of three months to improve their performance in Leicester and Leicestershire.
"If they fail to do so they should surrender the contract without any further payment or financial claim to the NHS and hand the contract over to another provider, preferably in the public sector.
"My message is clear - improve performance quickly or move on."
Health campaigner Zuffar Haq, a member of the Leicester Mercury Patients' Panel, said he would also like to see the contract cancelled.
He said: "The public is paying for services and not getting them.
"The public should not suffer in silence."
Mr Haq also called for better monitoring of the contract by the East Leicestershire and Rutland clinical commissioning group (CCG).
Ms Kendall added: "Unfortunately, the Care Quality Commission's report into Arriva comes as no surprise.
"I've taken up a number of constituency cases where patients have been at the sharp end of Arriva's poor service or have been let down by one of the company's third party subcontractors.
"Back in November 2013, Arriva's chief executive promised me that the company was working closely with commissioners to meet targets and improve its service to patients.
"This clearly hasn't happened. The CCG now needs to get a grip.
"Arriva must be made to step up and meet its obligations or step aside and let someone else get on with the job."
A spokesman for East Leicestershire and Rutland CCG, which manages the Arriva contract, said: "There is no doubt that performance is below acceptable levels. We recently agreed a range of new actions with Arriva.
"Many of the changes we've agreed have been directly influenced by what patients are telling us about their experiences.
"We hope to see the full impact of the changes by the end of October. In the meantime we are keeping the service under close scrutiny.
"If we don't see the expected improvements in Arriva's service and performance we will be carefully considering all options available to us."