Worldwide media outlets reported that Cambridge Analytica (CA), a data firm associated with Donald Trump's election campaign, had managed to extract data for about 50 million Facebook users, allowing it to create targeted and psychologically verified advertising content.
Mr Zuckerberg said he was "really sorry" for the "major breach of trust" and pledged to work to prevent data from being misused in future.
Zuckerberg closed the ads by saying: "I promise to do better for you".
A letter from Facebook co-founder and CEO Mark Zuckerberg appears in nine Sunday papers today in the form of a full-page advertisement. "If we can't, we don't deserve it", said the advert, signed by Facebook founder Zuckerberg.
The market value of the company has dropped by nearly United States dollars 58 billion within the span of one week, after news spread that it failed to maintain user data privacy, allowing the firm Cambridge Analytica to siphon the personal data of over 50 million users. "We're now taking steps to make sure this doesn't happen again", the ads said.
Whistleblower Christopher Wylie, who worked at Cambridge Analytica as its Director of Research, said the data was then used to influence the USA presidential election and UK Brexit referendum in 2016.
In all, because of extensive links of friends and associates to the 270,000 Facebook users, 50 million Facebook users may have had their personal data compromised.
The admission was written beneath the headline: "We have a responsibility to protect your information".
He said the social network planned to conduct an investigation of thousands of apps that have used Facebook's platform, restrict developer access to data, and give members a tool that lets them to disable access to their Facebook data more easily. We expect there are others.
Looking at Facebook's top 10 shareholders, we're unlikely to see many ditch their holdings in response to the latest scandal, with asset management companies accounting for the lion's share, nor are we likely to see any rumblings at the next AGM, barring the odd activist who may have brought some Facebook shares back in the day.
Finding out which apps received large amounts of information and banning them.
Finally, we'll remind you which apps you've given access to your information - so you can shut off the ones you don't want anymore.
"Thank you believing in this community", wrote Zuckerberg in his sign-off.