"You may have heard about a quiz app built by a university researcher that leaked Facebook data of millions of people in 2014," said the ads signed by Zuckerberg, referring to the political consultancy company accused of manipulating Facebook data during the 2016 US election.
"This was a breach of trust, and I'm sorry we didn't do more at the time. We're now taking steps to ensure this doesn't happen again," read the ads appearing in the UK's The Observer, The Sunday Times, Mail on Sunday, Sunday Mirror, Sunday Express and Sunday Telegraph, along with American newspapers The New York Times, Washington Post and Wall Street Journal.
The ads, featuring black text on a white background with the Facebook logo, said the social media company was now "limiting the data apps get" when users sign in, and was also "investigating every single app that had access to large amounts of data before" it fixed the problem.
According to the ad, Facebook will be reminding users which apps they'd previously given access to, giving them the opportunity to "shut off the ones you don't want anymore."
"I promise to do better for you," said Zuckerberg, who has come under harsh criticism for the scandal which sent the company's value plunging by almost $50 billion last week.
What is Cambridge Analytica accused of?
The ads come as Facebook announced last week it was suspending Cambridge Analytica's account over concerns the firm violated the social media site's policies. It followed reports from The New York Times and UK's The Observer newspaper (the Sunday edition of The Guardian) that Cambridge Analytica allegedly harvested the personal information of more than 50 million users.
Now Cambridge Analytica, which worked for Donald Trump's presidential campaign, is being accused of using that data in strategies for the US 2016 election.
Cambridge Analytica has repeatedly denied that the firm used any of Facebook's data in the work it did for Trump's campaign. The company also said it deleted the data when Facebook alerted them in 2015 that it had been improperly shared.
Facebook said the data in question was properly gathered a few years ago by psychology professor Aleksandr Kogan, who said he was using it for academic purposes.
But then the information was later transferred to third parties, including Cambridge Analytica. The transfer violated Facebook policies.
What is the fallout?
Scrutiny of Cambridge Analytica is growing as top officials from the firm claimed credit for President Donald Trump's stunning 2016 victory.
Last week, the embattled analytics company suspended its CEO, Alexander Nix, in the wake of a UK Channel 4 report showing undercover footage of Nix claiming he met Trump "many times" and that the company was responsible for a wide swath of the Trump campaign's activity.
On Friday, the company's offices in London were searched by enforcement officers from the United Kingdom's Information Commissioner's Office, following reports the organization had been harvesting data.
What's Steve Bannon got to do with it?
Cambridge Analytica was the creation of conservative billionaire Robert Mercer and conservative activist Steve Bannon, who later helped run the Trump campaign and served as chief strategist in the White House.
According to The Guardian, Bannon said at a conference Thursday that he "didn't even know about the Facebook mining."
Is there a Brexit connection?
On Sunday, the controversy surrounding Cambridge Analytica began to engulf to Britain's 2016 Brexit referendum.
Brexit campaigner Shahmir Sanni told Channel 4 that the British referendum's "Vote Leave" campaign spent over its legal limit by using the Canadian data firm called Aggregate IQ -- adding that the company had links to Cambridge Analytica.
British election law enforces a spending cap on donations, however Sanni claims a donation of £625,000 ($883,000) by Vote Leave to another Brexit group, "BeLeave," was funneled to AIQ.
Channel 4 says it has seen documents that it claims show multiple ties between AIQ and Cambridge Analytica's parent company, SCL.
However, attorneys for AIQ have distanced themselves from Cambridge Analytica, saying in a statement to Channel 4, "AggregateIQ has never entered into a contract with Cambridge Analytica."
An attorney for Vote Leave also told Channel 4 that the campaign had "twice been cleared on this matter by the Electoral Commission," but acknowledged the network's report presented new allegations and said it would investigate.