SAN FRANCISCO — Two women are suing Uber, alleging that inadequate driver background checks and monitoring left them and thousands of others vulnerable to sexual assault.

The women from Florida and California are not identified in the federal lawsuit filed Tuesday in San Francisco. Each alleges being sexually assaulted by Uber drivers who gave them rides home.

Uber says it received the complaint Tuesday and is reviewing it. “These allegations are important to us and we take them very seriously,” the ride-hailing firm said in a statement.

The lawsuit seeks class-action status and alleges that Uber has done nothing meaningful to stem an “exponential increase” in sexual harassment and assault reports. It alleges that Uber markets to young women traveling alone and puts profits over their safety.

“Over the last seven years, Uber has done everything possible to continue using low-cost, woefully inadequate background checks on drivers and has failed to monitor drivers for any violent or inappropriate conduct after they are hired,” the lawsuit states.

It asks the court for unspecified damages to compensate the women, and also seeks court-ordered safety measures including fingerprint background checks for drivers and a panic button on the Uber app that would alert the company and authorities to safety problems.

The lawsuit was filed by the New York firm Wigdor LLP, which is suing Uber in a separate case on behalf of a woman who was raped by an Uber driver in India. The firm also is suing Fox News on behalf of employees who allege race discrimination and sexual harassment.

Earlier this month, Uber pledged $5 million during the next five years to fund sexual assault prevention groups as well as train its own employees. Uber says the groups have helped it train 150 customer service agents for a team to deal with sexual assault reports. They’ve learned how to interview victims without being judgmental, and how to refer them to police and a crisis hotline.

Uber’s image has been tarnished by findings of sexual harassment of employees and multiple reports of drivers assaulting passengers. Other industries have also recently come under fire as women have been coming forward with complaints of sexual assault in Hollywood and other industries.