The iconic tech brand has been accused of failing to properly inform users that their profile data may have been obtained and then kept by Cambridge Analytica.
Facebook has already confirmed that it is blocking the firm while it investigates what's gone on.
However, the London-based company has not yet deleted the information.
Breaking his silence, he told CNN: "This was a major breach of trust, and I'm really sorry that this happened."
Zuckerberg said that he takes responsibility for what has happened, but said that Facebook will "learn" from there mistakes and endeavour to fix what went wrong.
He wrote on his own Facebook page: "I started Facebook, and at the end of the day I'm responsible for what happens on our platform. I'm serious about doing what it takes to protect our community. While this specific issue involving Cambridge Analytica should no longer happen with new apps today, that doesn't change what happened in the past. We will learn from this experience to secure our platform further and make our community safer for everyone going forward.
I want to thank all of you who continue to believe in our mission and work to build this community together. I know it takes longer to fix all these issues than we'd like, but I promise you we'll work through this and build a better service over the long term. (sic)"
Zuckerberg is under increasing pressure to open up about the social network site's recent conduct.
Adam Schiff, the highest-ranking Democrat on the House Intelligence Committee in the US, feels Zuckerberg - one of the world's wealthiest men - should be forced to face questions on the issue.
He said: "I think it would be beneficial to have him come testify before the appropriate oversight committees.
"And not just Mark but the other CEOs of the other major companies that operate in this space."
Elsewhere, former Presidential candidate Marco Rubio told NBC that some technology firms have behaved in a manner which suggests they think they're above regulators.
He explained that the growth of these firms has meant that they haven't always been held accountable for some of their behaviour.
Explaining his controversial viewpoint, Rubio said: "Their growth has been a lot faster than perhaps their ability to mature institutionally from within on some of these challenges that they're facing.
"I think another part about it is sometimes these companies grow so fast and get so much good press, they get up high on themselves that they start to think that perhaps they're above sort of the rules that apply to everybody else."