Facebook chief executive Mark Zuckerberg said he would not support a law that would give children greater privacy protections on sites like Facebook.

The social network's boss was testifying in a joint session of the Senate Judiciary and Commerce Committees over matters of data protection.

Sen. Ed Markey, a Democrat for Massachusetts, asked if Zuckerberg would "support a law to ensure that kids under 16 have this privacy bill of rights?"

Markey was proposing a so-called "bill of rights" for teenagers, which would in effect bridge the gap between Children's Online Privacy Protection Act (COPPA), which protects children under the age of 13, and additional measures that would help protect the privacy of American adults.

But Zuckerberg would not support the proposed law.

"I think it's an important principle," said the Facebook chief, and that it "deserves a lot of discussion." But when pressed, Zuckerberg said: "I don't know if we need a law."

Follow the Senate hearing: Senate tells Mark Zuckerberg: Don't let Facebook become a "privacy nightmare" | Read more: Trump-linked data firm Cambridge Analytica harvested data on 50 million Facebook profiles to help target voters | Data breach exposes Cambridge Analytica's data mining tools | How Cambridge Analytica used your Facebook data to help elect Trump | Analysis: On Facebook, Zuckerberg gets privacy and you get nothing

Zuckerberg has been in the hot seat in recent weeks following the Cambridge Analytica scandal. Last week, the company admitted that as many as 87 million users may have had their data "improperly shared" with the Trump-linked voter profiling data analytics firm.

It's been one of several fires the company had to put out since the news first broke.

The senator announced new legislation in a statement that would compel companies to obtain opt-in consent from users to use, share, and sell personal information, as well as notify users of how their data is being used.

The proposed law, dubbed the CONSENT Act, would also federally require web and tech companies -- like Facebook -- to notify users in the event of a breach, instead of reporting through state attorney generals.

"America deserves a privacy bill of rights that puts consumers, not corporations, in control of their personal, sensitive information," said Markey.

Facebook did not immediately return a request comment.