A spokesperson for the Tech company said: While we have today filed our appeal so that Londoners can continue using our app, we hope to continue having constructive discussions with Transport for London.
Uber has launched its appeal against Transport for London's decision to deny it a new operating licence in the capital.
An initial court hearing is expected on December 11.
Uber was required to begin its appeal by Friday or it would not be allowed to continue operating in London. In his open letter Khosrowshahi vowed to make things right with for Uber, so that it can still drive through the streets of London.
Despite the decision from TfL, and Uber's licence expiring on 30 September, Londoners will still be able to hail Uber cars until the full legal process is finalised, which could take up to a year or more.
Transport for London (TfL) refused to renew the firm's licence last month on the grounds of "public safety and security implications".
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Khosrowshahi and Brown met up earlier this month to discuss revoking the decision, and renewing Uber's license.
TfL cited concerns including Uber's approach to reporting criminal offences, its treatment of drivers, how it conducted medical and criminal checks on drivers, and whether software employed to evade regulation was being used in London.
The talks were described by both sides as "constructive". It has been attempting to overturn a judgment that drivers - about 40,000 of whom work for Uber in London - have rights to paid holiday and the minimum wage.
Uber hired Khosrowshahi from USA travel group Expedia in August, in the hope that he can steer the ride-sharing service away from the string of controversies.
An online petition to "save" Uber has garnered over 850,000 signatures.