The firm has denied misusing data and said it deleted the Facebook data after learning the information did not adhere to data protection rules.
Mr Zuckerberg wrote: “We have a responsibility to protect your data, and if we can’t then we don’t deserve to serve you. I’ve been working to understand exactly what happened and how to make sure this doesn’t happen again.
“The good news is that the most important actions to prevent this from happening again today we have already taken years ago.
“But we also made mistakes, there’s more to do, and we need to step up and do it.
“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.”