In part, Uber contests that it never had a relationship with the driver in question and that the alleged crime falls outside of the jurisdiction of U.S. courts.
The lawsuit was filed in January and relates to an incident in early December in which the woman, who was not identified, took a 45-minute Uber ride home. She fell asleep in the car and says she woke up to find the car parked in a secluded area and the driver on top of her. She was raped and assaulted for more than 30 minutes, according to the lawsuit.
With a building public outcry in India against the company, Uber called the assault "an abhorrent crime" and said it was committed to working with the New Delhi police to bring the perpetrator to justice.
In a late Monday filing in San Francisco, Uber drew a distinction between Uber Technologies, the U.S.-based parent company, and Uber B.V., the Dutch-based subsidiary that operates the Uber service in India.
"This case has everything to do with India and the Netherlands, and nothing to do with the United States," it said.
"Plaintiffs counsel has chosen to sue only Uber Technologies, which never had any relationship with Yadav, the alleged assailant," it said. "Yadavs only contractual relationship with any Uber entity was with Uber B.V., a Dutch company not party to this suit."
Uber, like many companies, runs its international operations through a subsidiary in the Netherlands. The company, which often champions the so-called sharing economy, benefits from this arrangement by reducing or avoiding taxes in many countries where it operates.
Uber B.V. is one of more than 100 distinct legal entities around the world that sit under the Uber brand, it said.
The company went on to argue that a California courtroom was not the right place for justice to be served as the assault took place in India between two Indian citizens.
The original lawsuit asks the court to order Uber to take affirmative steps to remedy the alleged conduct and prevent repeated occurrences.
Uber called the demands "impermissible, unworkable, and unprecedented" and said such an injunction would "rewrite Uber's business policies worldwide."
The plaintiff also seeks damages. A court case against Uber in the Netherlands or India, if successful, would likely be much less costly to the company than one in the U.S.
Uber's lawyers have asked for a hearing in July to argue that the case be dismissed.
Martyn Williams covers mobile telecoms, Silicon Valley and general technology breaking news for The IDG News Service. Follow Martyn on Twitter at @martyn_williams. Martyn's e-mail address is martyn_williams@idg.com