"We have a responsibility to protect your data, and if we can't then we don't deserve to serve you," Zuckerberg said in a statement on his Facebook page.
Over 50 million Facebook profiles were harvested by an app for data, which was then passed the information on to Cambridge Analytica. You can catch up with the full story here.
In his first statement, Zuckerberg set out steps that the social network would take to avoid a repeat of the abuse and give people a better idea of how their data are being used.
Facebook will investigate all apps that had access to large amounts of data and will audit apps with "suspicious activity," Zuckerberg said. He added that the company would restrict developers' access to data.
And Facebook will implement a new tool at the top of the News Feed that will show users which apps they are using and give them an easy way to revoke permissions to data.
While Zuckerberg didn't say the word "sorry" in his initial Facebook post, the CEO did apologize in an interview with CNN.
"So this was a major breach of trust and I'm really sorry that this happened," Zuckerberg said, adding that the company's "responsibility now is to make sure that this doesn't happen again."
Following revelations of the scandal, the hashtag #DeleteFacebook circulated online. Even Brian Acton, the co-founder of WhatsApp, a company that Facebook bought for $19 billion in 2014, tweeted the hashtag.
Analysts have been concerned about the knock-on effect the fiasco would have on user numbers, but Zuckerberg said he had not seen lots of people leaving the social network.
"I don't think we've seen a meaningful number of people act on that, but, you know, it's not good," Zuckerberg told The New York Times on Wednesday about the hashtag.
"I think it's a clear signal that this is a major trust issue for people, and I understand that. And whether people delete their app over it or just don't feel good about using Facebook, that's a big issue that I think we have a responsibility to rectify."
Some analysts believe that tougher regulation is on the way for social media companies, which could be moved forward by the Cambridge Analytica scandal. Zuckerberg said he would be open to regulation.
"I actually am not sure we shouldn't be regulated. I think in general, technology is an increasingly important trend in the world and I actually think the question is more, what is the right regulation, rather than 'yes or no, should it be regulated?'" Zuckerberg told CNN.
The Facebook CEO said there is "ads transparency regulation" that he would "love to see."
"If you look at how much regulation there is around advertising on TV and print, it's just not clear why there should be less on the internet. We should have the same level of transparency required," Zuckerberg said.
Zuckerberg said he would be open to testifying in front of Congress if asked.
"So, if it is ever the case that I am the most informed person at Facebook in the best position to testify, I will happily do that," Zuckerberg told Wired in an interview Wednesday.
"But the reason why we haven't done that so far is because there are people at the company whose full jobs are to deal with legal compliance or some of these different things, and they're just fundamentally more in the details on those things.
"So, as long as it's a substantive testimony where what folks are trying to get is as much content as possible, I'm not sure when I'll be the right person. But I would be happy to if I were."
"Yes. We're going to tell anyone whose data may have been shared," Zuckerberg said when asked if he would notify people about the incident.
The CEO did admit that there is a "question" of whether the company has the exact records in its system about who users' friends were on the day when the data was accessed in 2014.
"We're going to be conservative on that and try to tell anyone whose data may have been affected, even if we don't know for certain that they were," Zuckerberg told The New York Times.
Facebook was criticized for allowing fake news and Russian propaganda on its platform during the 2016 presidential elections. Other elections and votes around the world have taken place since then, and with the U.S. midterms coming in November, Zuckerberg said he feels comfortable with the social media network's ability to police more effectively.
"I feel a lot better about the systems now. At the same time, I think Russia and other governments are going to get more sophisticated in what they do, too. So we need to make sure that we up our game," Zuckerberg told The New York Times.
"This is a massive focus for us to make sure we're dialed in for not only the 2018 elections in the U.S., but the Indian elections, the Brazilian elections, and a number of other elections that are going on this year that are really important."