NEW YORK — Fair housing groups filed a lawsuit in federal court Tuesday saying that Facebook continues to discriminate against certain groups, including women, disabled veterans, and single mothers, in the way that it allows advertisers to target the audience for their ads.

The suit comes as the social network is scrambling to deal with an international crisis over the misuse of data belonging to 50 million of its users.

Facebook, an advertising ­behemoth with more than 2 ­billion users a month, provides advertisers with the ability to ­customize their messages and target who sees them by selecting from preset lists of demographics, likes, behaviors, and interests, while excluding others.

Pet food companies, for example, could send their ads specifically to people who had indicated an interest in dogs, while excluding cat and bird fanciers.

When it comes to housing and employment ads, Facebook, in response to criticism over the last 17 months, has repeatedly promised that it would crack down on advertisers who use those same tools to show housing or employment ads to whites ­only.

But in the lawsuit filed Tuesday in US District Court in Manhattan, the National Fair Housing Alliance and affiliated groups in New York, San Antonio, and Miami contend that Facebook’s advertising platform “continues to enable landlords and real estate brokers to bar families with children, women, and others from receiving rental and sales ads for housing.’’

Diane L. Houk of Emery Celli Brinckerhoff & Abady, a lawyer who worked on the lawsuit, said the groups want the court to ­require Facebook to take action.

“We want the court to order Facebook to develop a plan to remove any ability for advertisers to access Facebook’s checklists for excluding groups of people in the posting of housing-related ads,’’ Houk said. “Because of Facebook’s impact on the housing market, we’ll ask the court to implement a plan of community education and outreach to housing providers to inform them of their obligation not to discriminate.’’

The suit says Facebook’s ­actions are a violation of the Fair Housing Act, which makes it ­illegal to publish housing ads that indicate preferences or limitations based on race color, religion, handicaps, familial status, or national origin.

“Facebook’s ability to customize an online audience for advertisements based on its vast trove of user data has made it the biggest advertising agency in the world — the advertising platform of choice for millions of businesses,’’ the lawsuit states. “But Facebook has abused its enormous power.’’

The criticisms go directly to the heart of Facebook’s business. The social network earned nearly all of its more than $40 billion in revenue in 2017 by selling ads on its network.

Facebook did not return a ­request for comment.

To test its case, the National Fair Housing Alliance created an ad for a fictitious apartment rental in Washington, D.C., using Facebook’s features to exclude “corporate moms,’’ “stay-at-home moms’’ and other categories that would eliminate women from the ad’s potential audience. Facebook estimated that the ads would reach 48,000 to 820,000 people, the lawsuit said.

In New York, the Fair Housing Justice Center created an ad for a rental apartment by selecting “no kids’’ and “men’’ from the inclusion list and “moms of grade school kids’’ and other groups from the exclusion list. Facebook estimated that the ad would reach 280,000 people.

The lawsuit says that Facebook also provides “interests’’ categories for housing ads that permit a landlord or real estate agent to exclude users based on disability-related factors, such as “Interest in Disabled Parking ­Permit,’’ or “disabled veteran,’’ and on the basis of national origin, by eliminating those with, say, an “Interest in Telemundo,’’ the Spanish language television network, or English as a second language.

“The way people find housing in 2018 is radically different than when the Fair Housing Act was passed in 1968,’’ said Robert Schwemm, a law professor at the University of Kentucky and author of “Housing Discrimination: Law and Litigation.’’

But, he added, “the Fair Housing Act makes it illegal to target certain groups while excluding others.’’

“The courts have taken discriminatory housing ads very seriously,’’ he said.