The 26-year-old woman accuses the firm of failing to ensure passengers' safety and is seeking unspecified damages.

In a statement, Uber said that it was co-operating with authorities to ensure the 'perpetrator is brought to justice'.

The accused driver, Shiv Kumar Yadav, is currently on trial on rape and kidnapping charges.

According to the woman, Yadav drove her to a secluded area and raped her. He has denied the charges.

The woman's lawyer filed the lawsuit in San Fransisco, where the firm is based, and asked the court to protect her identity.

Uber's service is described in the lawsuit as a 'modern-day equivalent of electronic hitchhiking.'

The firm's spokeswoman, Nairi Hourdajian, in a statement said the company's "deepest sympathies remain with the victim of this horrific crime."

"We are co-operating fully with the authorities to ensure the perpetrator is brought to justice."

In early December 2014, Uber and several other web-based taxi firms were banned in Delhi, for failing to carry out adequate driver checks.

Last week Uber restarted services in Delhi, saying it had applied for a radio taxi licence and would improve safety by introducing features such as an "in-app emergency button".

The company has apologised for the incident and acknowledged that it "must do better".

But it has defended the way it checks drivers, and said it expected to have completed about two million background checks worldwide by the end of 2014.