http://www.bbc.co.uk/news/business-41384499London Mayor Sadiq Khan has asked the city's transport regulator to be available to meet Uber's boss after the firm apologised.
Uber chief executive Dara Khosrowshahi said he was sorry for the "mistakes we've made" after the taxi-hailing firm lost its London licence.
He said in an open letter that Uber would appeal against the city's decision, but accepts it "must change".
On Friday, Transport for London (TfL) denied Uber a new licence to operate.
Mr Khan said: "I welcome the apology from Dara Khosrowshahi, the Uber CEO. Obviously I am pleased that he has acknowledged the issues that Uber faces in London.
"Even though there is a legal process in place, I have asked TfL to make themselves available to meet with him.
TfL cited concerns over public safety and security in its decision not to renew Uber's London licence.
However, Uber says it has followed the regulator's rules and works closely with the Metropolitan Police.
Mr Khosrowshahi, who took over at Uber 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.
"On behalf of everyone at Uber globally, I apologise for the mistakes we've made."
In a letter addressed to Londoners, the new Uber boss said the firm "won't be perfect, but we will listen to you".
Dara Khosrowshahi took over as Uber boss last month after Travis Kalanick resigned
Earlier, the Mayor of London said Uber had put "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 Today Programme.
Over 750,000 people have signed an online petition to keep Uber operating
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.
if i was a betting man i would wager that Uber will promise all sorts of changes in exchange for a renewal of license and TFL will decide they have to give it to them especially considering the amount of money involved and what that would do for TFL finances
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