Councillor Shaukat Ali said a delay in testing and "mixed messages" from Tory-led Dudley Council may be responsible for the spike.
But leader Councillor Patrick Harley has hit back – claiming the Labour councillor had offered "nothing" in the fight against the virus.
Figures for the borough, in the seven days up to November 14, show a rate of 568.7 infections per 100,000 people – more than double the national infection rate.
More Covid-19 coverage:
Councillor Ali, Labour's health chief on the authority, claimed the mobile testing unit at Merry Hill "lacked testing capacity" from the start.
He said: "Dudley Council leaders' mixed messages, late provision of testing facilities and delayed lockdown may have led to this significant increase in cases.
"In the space of one week, we heard the council leader say he disagreed with a strengthened lockdown and then agree with it, which is not good when what the people of Dudley need most is clarity.
"We also raised the lack of testing capacity some time ago and asked for resources to be diverted from the failing private companies responsible for testing to local councils.
"This all fell on deaf ears resulting in the higher number of positive cases we are now seeing in the community, schools and colleges."
Councillor Harley, leader of the council, dismissed the claims and accused Councillor Ali of making "silly comments" and putting himself first.
He said: "Our testing rate has increased significantly – 76 per since start of October – in recent weeks.
"That is the primary factor in the increase in cases. Nationally, trends show that there is a correlation between increased figures and increased testing.
"As a council we have just been nominated for a national award for the quality of our communications during the pandemic. You don't get those nominations for sending out mixed messages.
"Our message throughout has been clear and consistent, that people must follow the national guidance to keep themselves and those around them safe.
"People understand unlike Councillor Ali that we are operating in a fast moving and fluid situation but there has not been any mixed messaging whatsoever.
"Clearly yet again Councillor Ali puts his own self importance with his silly comments to media whilst offering nothing to assist the borough in tackling this pandemic.
"Lucky for the people of Dudley they stopped listening to what Labour had to offer years ago."