London Mayor Sadiq Khan has asked the city's transport regulator to meet Uber's boss after the firm apologised for the "mistakes" it has made.
Uber chief executive Dara Khosrowshahi issued the apology after the taxi-hailing firm lost its London licence.
Mr Khosrowshahi said in an open letter that Uber would appeal against the city's decision, but accepted the company "must change".
On Friday, Transport for London (TfL) denied Uber a new licence to operate.
Uber has said it wants to meet TfL to discuss the regulator's concerns over public safety and security.
The London mayor welcomed Mr Khosrowshahi's apology, saying: "Even though there is a legal process in place, I have asked TfL to make themselves available to meet with him."
In deciding not to renew Uber's licence beyond the end of September, TfL cited concerns about the firm's treatment of criminal offences, medical certificates, and drivers' background checks.
When asked about a possible meeting, a spokesman for TfL said: "We are always available and happy to meet at any time."
Uber says it has followed the regulator's rules and works closely with the Metropolitan Police.
The firm, which is used by an estimated 40,000 drivers and 3.5 million customers in London, also says it will continue operating while its appeal is heard.
Mr Khosrowshahi, who took over at the firm less than a month ago, wrote on Monday: "While Uber has revolutionised the way people move in cities around the world, it's equally true that we've got things wrong along the way."
In a letter addressed to Londoners, the new Uber boss said the firm "won't be perfect, but we will listen to you".
"On behalf of everyone at Uber globally, I apologise for the mistakes we've made," Mr Khosrowshahi said.
Earlier, the mayor of London accused Uber of putting "unfair pressure" on TfL, with an "army" of PR experts and lawyers.
Mr Khan, who is also chairman of TfL, told the BBC: "What you can't do is have a situation where unfair pressure is brought on a quasi-judicial body, where there are officials working incredibly hard.
"I appreciate Uber has an army of PR experts, I appreciate Uber has an army of lawyers - they've also made aggressive threats about taking us to court."
When asked if he would meet Uber personally, the mayor said it would be "improper for politicians to interfere with a quasi-judicial matter".
The mayor's office said Mr Khan would not be directly involved in discussions or meetings with Uber if they took place.
While Mr Khan chairs the TfL board, according to the organisation he was not involved in the process of deciding whether to issue Uber with a licence.
That is handled by TfL's taxi and private hire department.
Uber is keen to hold talks with officials from that department "as soon as possible", Fred Jones, a senior executive with Uber in the UK, told the BBC's Today Programme.
Mr Jones said that Uber was "not clear" about the issues raised by TfL when it denied the company a licence.
One of the points raised by TfL was Uber's "approach to how Enhanced Disclosure and Barring Service (DBS) checks are obtained" for its drivers.
That part of the process was not even handled by Uber, said Mr Jones. Instead, the drivers organised their own DBS check and took that paperwork to TfL.
TfL then reviews that application before giving the driver a licence allowing them to drive for Uber.
TfL would not elaborate further on its issue with the way in which Uber organises DBS checks, because that would be likely to come up when Uber appealed against the decision.
It would only repeat that it was Uber's "approach" to DBS checks that was the problem.
More than 750,000 people have signed an online petition in a bid to keep Uber operating in London after its licence expires on 30 September.