Two people familiar with the matter, who spoke on the condition of anonymity because the discussions were confidential, said that Mr. Zuckerberg planned to address the Cambridge Analytica situation and the larger data privacy issues with a public statement on Wednesday. The statement will be aimed at rebuilding trust with users, one of the people said. In the past week, one of the people said, Mr. Zuckerberg has spent significant time hunkered down with a small group of engineers to discuss how to make Facebook’s users more secure, with more control of their data.

Kate Losse, an early Facebook employee and Mr. Zuckerberg’s former speechwriter, said that the Cambridge Analytica controversy was different from previous Facebook privacy scandals, in that it was about an issue at the core of the company’s business model that will not be easily remedied: the disclosure of Facebook data to outside sources through its third-party developer platform.

“My guess is that what is giving Zuckerberg pause at this point is the question of how to acknowledge and explain this state of affairs while at the same time mitigating the concerns that will come from people finally understanding how this all worked,” she said.

Mr. Zuckerberg is no stranger to speaking out during times of company crisis. In 2006, users rebelled after Facebook introduced the first version of its news feed, which showed users for the first time what their friends were doing on the social network. As groups formed to protest what they felt was an incursion on their privacy, Mr. Zuckerberg posted a peacemaking note on his Facebook page.

“Calm down. Breathe. We hear you,” he wrote.