Two companies that have been on every timeline for the last few days are Cambridge Analytica, the political data firm with ties to President Trump’s 2016 campaign and Facebook that provided the data to the former. In today’s developments, Cambridge Analytica suspended its chief executive, Alexander Nix, on Tuesday, amid the furor over the access it gained to private information on more than 50 million Facebook users.The decision came after a television broadcast in which Mr. Nix was recorded suggesting that the company had used seduction and bribery to entrap politicians and influence foreign elections.

The suspension marked a new low point for the fortunes of Cambridge Analytica and for Mr. Nix, who spent much of the past year making bold claims about the role his outfit played in the election of Mr. Trump. The company, founded by Stephen K. Bannon and Robert Mercer, a wealthy Republican donor who has put at least $15 million into it, offered tools that it claimed could identify the personalities of American voters and influence their behavior. So-called psychographic modeling techniques, which were built in part with the data harvested from Facebook, underpinned Cambridge Analytica’s work for the Trump campaign in 2016. Mr. Nix once called the practice “our secret sauce,” though some have questioned its effectiveness.

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But in recent days, the firm has found itself under increased scrutiny from lawmakers, regulators, and prosecutors in the United States and Britain following reports in The New York Times and The Observer of London that the firm had harvested the Facebook data, and that it still had a copy of the information.

The reports quickly put Mr. Nix in the crosshairs of a Parliamentary committee investigating fake news and Russian interference in Britain’s referendum to exit the European Union. Earlier this month, he told the committee that Cambridge Analytica had never obtained or used Facebook data — a statement that the firm itself has contradicted in recent days.

Announcing its chief executive’s suspension, Cambridge Analytica said in a statement that “in the view of the board, Mr. Nix’s recent comments secretly recorded by Channel 4 and other allegations do not represent the values or operations of the firm and his suspension reflects the seriousness with which we view this violation.” The company said it had asked Alexander Tayler, its chief data officer, to serve as its acting chief executive. Mr. Tayler trained as a chemical engineer and joined Cambridge Analytica in 2014 as its lead data scientist, according to his LinkedIn profile.

At the same time, the company said it was launching an independent investigation of Mr. Nix’s comments and the allegations facing the firm. The company said it had hired a lawyer, Julian Malins, to lead this investigation, the findings of which the board will share publicly in due course. It added: “The board will be monitoring the situation closely, working closely with Dr. Tayler, to ensure that Cambridge Analytica, in all of its operations, represents the firm’s values and delivers the highest-quality service to its clients.”

Facebook, too, has sought to avoid the spotlight but also found itself under a similarly unwelcome glare. In the United States, the Federal Trade Commission said on Tuesday that it had opened an investigation into whether Facebook violated an agreement with the agency on data privacy.

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In addition, Eric T. Schneiderman, the attorney general of New York, said the state was joining Massachusetts in an investigation into whether the company failed to protect the privacy of users in those states. Their attorneys general have demanded that Facebook hand over information about its interactions with Cambridge Analytica. “Consumers have a right to know how their information is used — and companies like Facebook have a fundamental responsibility to protect their users’ personal information,” Mr. Schneiderman said.

In Britain, Damian Collins, the chairman of the Digital, Culture, Media and Sports Select Committee of the House of Commons, which is running the inquiry into the fake news, called on Mark Zuckerberg, Facebook’s chief executive, to give evidence to Parliament. In a letter, Mr. Collins said that previous answers from Facebook officials about the misuse of data had been misleading. “It is now time to hear from a senior Facebook executive with the sufficient authority to give an accurate account of this catastrophic failure of process,” the letter said, adding, “I hope that this representative will be you.”

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