"I'll have my team follow up with you so that way we can have this discussion across the different categories where I think this discussion needs to happen", Mr Zuckerberg told a joint hearing by the US Senate's Commerce and Judiciary committees, when asked what regulations he thought were necessary.
He added that users are able to view a list of what third-party apps that had downloaded that may have access to their data, and that the data-selling practices that led to Cambridge Analytica using people's information in attempts to skew elections had been shut down in 2015.
Cambridge Analytica used 87 million Facebook user profiles for a quiz app.
It couldn't be easier to watch Mark Zuckerberg's congress live stream.
Facebook CEO Mark Zuckerberg acknowledged overnight that regulation of social media is "inevitable" and disclosed that his own personal information has been compromised by malicious outsiders.
Facebook's business model is, as the executive clarified, that it runs ads, and it does that by letting companies target people based on their information. No, Facebook doesn't sell your data. "But at the same time it doesn't seem like future activities are prevented".
"When we heard back from Cambridge Analytica that they had told us that they weren't using the data and deleted it, we considered it a closed case", Zuckerberg said.
His admission that even the company's tech-savvy founder was unable to protect his own data underscored the problem Facebook has in persuading skeptical lawmakers that users can easily safeguard their own information and that further legislation governing Facebook is unnecessary. For most of our existence, we focused on all of the good that connecting people can do. He offered no details, citing a concern about confidentiality rules of the investigation.
A house hearing examining the company's privacy policies and the role Facebook played as Russians intervened in the 2016 election has begun. Representative Joe Barton, a Texas Republican, pulled out his phone and read a constituent's question about Facebook silencing conservative commentators known as Diamond & Silk.
Much of the effort was aimed at denigrating Democrat Hillary Clinton and thereby helping Republican Trump, or simply encouraging divisiveness and undercutting faith in the USA system.
In prepared testimony Mr Zuckerberg said the company had made "mistakes" that allowed the leak of data to Cambridge Analytica, the analytics firm that worked for the Trump presidential campaign.
Some representatives think Facebook has violated its consent decree with the Federal Trade Commission.
Democratic senator Sheldon Whitehouse called out a problem with this plan, though: The legions of United States shell companies that hide their ultimate owner.
The hearings that ended on Wednesday revealed no consensus among us lawmakers about what kind of privacy legislation they might want to pursue if any, and no timeline for action.
At the Senate hearing, Zuckerberg had said he was willing to consider new restrictions, and agreed to send suggestions to Congress. Senators signaled they may move to rein in Facebook, which has thrived as part of an online industry that's largely escaped regulation.
Facebook rose less than 1 percent Wednesday as Zuckerberg was questioned by the House panel. "It was my mistake, and I'm sorry", he said. He had no response when asked how a non-Facebook member could remove information without signing up for the service.