The reports prompted concerns among lawmakers and regulators in Europe and the United States about whether Facebook had a proper handle on the data of its more than 2.2 billion users worldwide. The revelations have spawned months of crisis for the Silicon Valley company, on top of other issues that the social network has faced, such as how it was manipulated by Russians to interfere in elections. Facebook’s top executives, including its chief executive, Mark Zuckerberg, have vowed to improve the site.

Even so, it will likely take many more months to resolve the fallout from Cambridge Analytica. In some places, regulators and lawmakers have moved swiftly. In Britain, Facebook was hit in July with the maximum possible fine of 500,000 pounds, or about $660,000, for the improper harvesting of its users’ data.

At the time, the Information Commissioner’s Office in Britain said that its inquiry had determined that “Facebook contravened the law by failing to safeguard people’s information. It also found that the company failed to be transparent about how people’s data was harvested by others.”

In the United States, legal and regulatory action has been slower. Earlier this year, the Justice Department and the F.B.I. began investigating Cambridge Analytica, which is now defunct. In July, Facebook said it faced an expansion of federal investigations into its sharing of user data with Cambridge Analytica.

Several state attorney general offices have also announced investigations into Facebook because of Cambridge Analytica. In the lawsuit brought by Mr. Racine on Wednesday, he said the Facebook data of roughly half of the District of Columbia’s residents had been exposed by Cambridge Analytica’s harvesting. Mr. Racine also said the social media company misled people about the security of their data, and made it difficult to control privacy settings on the platform.