London Mayor Sadiq Khan has welcomed an apology by the chief executive of Uber, setting the scene for crunch talks between Transport for London and the ride-hailing giant, which was last week stripped of its licence to operate in the city.

In an open letter published on Monday, Uber CEO Dara Khosrowshahi pleaded for his company to be allowed to continue operating in the capital – one of its most important European markets – after its licence expires on 30 September.

On Friday, TfL said that it deemed the company “not fit and proper to hold a private hire operator licence” and said its approach and conduct “demonstrate a lack of corporate responsibility in relation to a number of issues which have potential public safety and security implications”.

On Monday, in a one-page letter that he tweeted from his personal account, Mr Khosrowshahi admitted that the company had “got things wrong”. He apologised for the “mistakes … made” and asked that TfL, of which Mr Khan is the chairman, give Uber the opportunity “to make things right”.

“We won’t be perfect, but we will listen to you; we will look to be long-term partners with the cities we serve; and we will run our business with humility, integrity and passion,” Mr Khosrowshahi said.

Mr Khan, who earlier in the day implied that he was not prepared to meet with Uber, on account of it being improper for a politician to interfere in what he described as a “quasi-judicial matter”, welcomed the comments.

“Obviously I am pleased that [Mr Khosrowshahi] has acknowledged the issues that Uber faces in London,” he said. “Even though there is a legal process in place, I have asked TfL to make themselves available to meet with him.”

Uber on Friday said it was “astounded” by TfL’s decision. It has since confirmed that it is challenging the move.

Tom Elvidge, general manager of Uber in London, launched an online petition to challenge TfL’s move on Friday. By Monday evening it had already garnered almost 770,000 virtual signatures.

Mr Khosrowshahi recently joined Uber from Expedia, after his predecessor, Travis Kalanick – who founded Uber about eight years ago – resigned in the face of shareholder outrage over company culture.

In addition to the TfL ban, Mr Khosrowshahi is also juggling legal suits alleging the company stole self-driving technology from Google parent Alphabet and a bribery investigation in Asia.

TfL on Friday gave the company 21 days to appeal the decision not to extend the licence, during which time Uber can continue to operate.

An estimated 3.5 million people use Uber in London and if the decision stands, it could put more than 40,000 licensed drivers out of work.