Councillor Sayonara Luxton, chairman of the healthoverview and scrutiny committee, believes an extended consultation would ensure transparency and fairness.
The Leicester, Leicestershire and Rutland HealthOverview and Scrutiny Committee called for a review into how recommendations were reached by the Joint Committee of Primary Care Trusts (JCPCT).
In a draft report by the HealthOverview and Scrutiny Committee, it claims millions of pounds are being wasted as too few people use walk-in centres and minor injury units.
At a meeting of the the Joint HealthOverview and Scrutiny Committee, Dr Mike Bewick, from NHS England, said he apologised for the inconvenience caused by the suspension but not for the decision.
On Friday the Leicester, Leicestershire and Rutland Joint Health and Overview Scrutiny Committee said it had sent a document to Secretary of State for Health Jeremy Hunt to appeal against moving children's heart surgery services.