Sadiq Khan warned Transport Secretary Chris Grayling a "huge increase" in mini cabs in the city is causing increased congestion, pollution and leaving many drivers struggling to earn a living.
He said the number of private hire drivers in London has almost doubled from 60,000 in 2011 to 110,000.
Officials in New York last week approved a cap on the number of licences for ride-hailing cars, which will impact app-based services such as Uber and Lyft.
Of the 96,326 black for-hire vehicles in New York, 77,571 (81%) are affiliated with Uber, according to figures obtained by the New York Post from the city's Taxi and Limousine Commission.
"It's time for the big corporations to take a back seat and for working people to take the wheel," Mayor Bill de Blasio said as he signed the bill at City Hall, aimed at tackling congestion and addressing driver wages.
Mr Khan described it as a "necessary step".
In his letter to the Cabinet minister, he wrote: "Unlike New York, I don't have the power to cap the number of private hire vehicles in London.
"I am writing to again urge the government to grant me that power as the Mayor of London - alongside appropriate restrictions on cross-border hiring, to enable Londoners, like New Yorkers, to breathe better air and live in a less congested city."
An Uber spokesman said: "Uber is committed to helping address congestion and air pollution and we strongly support the mayor's ultra low emission zone.
"Already more than half of the miles travelled with Uber are in hybrid or electric vehicles.
"By competing with private cars, getting more people into fewer vehicles and investing in our clean air plan, we can be a part of the solution in London."
In June, Westminster Magistrates' Court overturned a ban on Uber imposed by Transport for London late last year and granted the firm a 15-month licence to operate in London.
Mr Khan had argued Uber was not "a fit and proper" holder of such a licence amid concerns about the company's approach to reporting serious criminal offences, how drivers' medical certificates were obtained, how criminal record checks were carried out and its use of technology which allegedly helped it evade law enforcement officials.
Uber admitted it had made "serious mistakes" and that TfL was correct in its September decision, but told an appeal hearing it had made "wholesale" reforms.
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Earlier this month, ride-hailing app Ola unveiled its plans to launch in the UK after obtaining licences to operate in Greater Manchester and South Wales.
The Indian firm said it was working with local authorities to expand across the UK by the end of 2018.