London Mayor Sadiq Khan has asked the city's transport regulator to be available to meet Uber's boss after the firm apologized.
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.
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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 boss said the firm "won't be perfect, but we will listen to you".
Earlier, the Mayor of London said Uber had put "unfair pressure" on Transport for London (TfL), with an "army" of PR experts and lawyers.
Mr Khan, who is also chairman of TfL, told the BBC: "What you cannot do is have a situation where an 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."
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.
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.
Read also:  Uber loses its licence to operate in London
 More than 500,000 sign petition to save Uber as firm fights London ban
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