But though she could really use the ride-hailing app, Ms. Joseph said she does not bother because Uber has so few wheelchair-accessible cars to dispatch. “It’s plain unfair,” said Ms. Joseph, 41, who relies on a wheelchair.

Now, Ms. Joseph is part of a class-action lawsuit accusing Uber of discriminating against New York City riders with disabilities by providing scant access to wheelchair-accessible cars at a time when ride-hailing apps are becoming a common alternative to public transit in the city. The lawsuit was filed on Tuesday in State Supreme Court in Manhattan by Disability Rights Advocates, a nonprofit organization.

While Uber offers wheelchair-accessible cars through its UberWAV service, the lawsuit claims that these special cars, which typically have lifts and ramps for mobility devices, account for a tiny fraction of the 58,000 for-hire cars dispatched by Uber in New York City’s five boroughs. Moreover, this already limited pool of cars can be used for other riders, and vehicles may be unavailable when needed by those with disabilities, the lawsuit said.

The result is that “even when an UberWAV vehicle is technically available, because so few exist, there are typically frequent and lengthy delays,” the lawsuit stated. It added, “As such, people who use wheelchairs and use UberWAV must contend with missed appointments, being late for events and other stress and inconvenience.”

The lawsuit was filed on behalf of a coalition of advocacy groups and individuals, including the Brooklyn Center for Independence of the Disabled, Taxis for All Campaign and Disabled in Action of Metropolitan New York. It follows two other discrimination lawsuits involving handicapped travelers filed this year against the Metropolitan Transportation Authority over the scarcity of elevators and electric lifts in the subway system.

The Taxis for All Campaign previously led a similar discrimination lawsuit over yellow taxis, which resulted in a settlement that requires half of all yellow taxis to be wheelchair accessible by 2020.

Today, there are 1,859 yellow taxis and 655 green taxis, which primarily serve northern Manhattan and the other boroughs, that are wheelchair accessible. Last week, the city’s Taxi and Limousine Commission proposed broad new requirements for wheelchair-accessible service for the entire for-hire industry, which would include Uber and the other ride-hail companies. These requirements, which will be reviewed at a public hearing in September, would have to be approved by the commission’s board before they could go into effect.

Alix Anfang, a spokeswoman for Uber, said the company had already voluntarily taken steps to serve riders with disabilities. In 2016, it started a pilot program for wheelchair-accessible cars that has since expanded to nearly 200 vehicles. (The lawsuit filed against Uber said there were fewer than 100 accessible cars, based on city data.)

Ms. Anfang said the company had offered incentives to drivers of wheelchair-accessible cars, including offering $10 for each completed trip, $500 after completing 40 trips in the first week, and reduced commissions paid to Uber. The company has also called for a city law that would add a 5-cent ”accessibility fee” on all black car and livery car trips to raise money for a fund, which would be administered by the city, to provide financial incentives for companies and services that provide rides in wheelchair-accessible cars.

“Uber’s technology has expanded access to reliable transportation options for all riders,” Ms. Anfang said. “While there is certainly more work to be done, we will continue advocating for a solution that offers affordable, reliable transportation to those who need a wheelchair accessible vehicle.”

Still, it is not enough for some riders with disabilities and their advocates. Ms. Joseph, who lives in Queens and works in Brooklyn, said she had friends and colleagues who had tried to hail an Uber car, only to find long wait times if the car arrived at all. She said she was limited by having few other good options for getting around the city.

“I feel frustrated because I have to plan my day,” she said. “I can’t do things on a whim. I have to plan it days in advance.”

The lawsuit claims that Uber, in discriminating against riders with disabilities, has violated the city’s human rights laws; the plaintiffs ask that the court require Uber to “develop and implement a remedial plan to ensure full and equal access to its services for riders who require accessible transportation.”

“Uber claims it’s a revolutionary company, but it’s engaged in old-fashioned discrimination against people with disabilities from its first day in New York City,” said Joe Rappaport, executive director of the Brooklyn Center for Independence of the Disabled. “Our lawsuit against Uber’s discrimination makes it clear: It’s 2017, not the 1950s, when it comes to equal access to transportation.”

The lawsuit is the latest challenge for a troubled company, whose chief executive, Travis Kalanick, was forced out amid widespread criticism over the company’s handling of sexual harassment, executive misbehavior and its internal culture. Uber, which has a fraught relationship with its drivers, recently reversed course to allow passengers to tip their drivers through the Uber app.