Car-sharing startup Uber on Friday bragged it rang in the New Year with two million rides, many of them apparently to revellers heading home in early morning hours.

And while demand for rides spiked from one to two in the morning in most cities where Uber operates, partiers in Paris didn't put pressure on the service until after 4 am local time (0300 GMT).

The Uber smartphone application was downloaded more than 20,000 times after midnight on New Year's Eve, the company added.

Use of Uber through the night hit a peak of 58 rides reaching their destinations a second, according to the San Francisco-based startup.

In December, Uber scrambled to allay fears that executives at the hot car-sharing startup are gunning for journalists and spying on riders.

The controversy widened when a BuzzFeed report indicated that executives at Uber had taken liberties with access to a "God View" that showed where riders and their drivers were located at any given time.

The firm, which lets customers order and pay for taxis or private vehicles via smartphones, has been unofficially valued in the range of $25 billion to $30 billion based on funding rounds.

Its smartphone app connects users with local drivers and the company charges a commission for each ride.

Founded in 2009, Uber is now present in more than 200 cities and in 45 countries.

The company's rapid expansion has caused tensions with traditional taxi drivers, especially in Europe.