Lives are at risk because of a delay in transferring responsibility for the underground to Transport for London, according to Ken Livingstone.
The mayor was expected to take control of the service by summer, but legal technicalities may delay the transfer until Christmas.
Mr Livingstone said as the existing London Underground (LU) management was on its way out, it might not be "on the ball as far as safety is concerned".
But LU has described the accusation as "insulting" and untrue.
For the mayor to suggest that managers are putting their future careers
above the safety of the Tube is as insulting as it is untrue
London Underground spokeswoman
The mayor dropped his legal challenge to the privatisation of Tube maintenance in February to gain control.
He said the present management did not have his confidence and "need to be replaced as quickly as possible."
"My concern is that the sort of disaster we saw on the Central Line (last month) could happen somewhere else on the underground," he said.
He plans to lobby the government to ensure the transfer goes ahead as quickly as possible.
But a LU spokesman said managers were trying to ensure a speedy transfer while continuing to run a "safe and efficient" service.
She added: "For the mayor to suggest that managers are putting their future careers above the safety of the Tube is as insulting as it is untrue."
A total of 32 passengers were hurt when a Central Line train derailed at Chancery Lane last month.
The line has been closed while trains are modified following the accident which was caused by a traction motor falling from under the train on to the track, derailing the carriages.