In a letter to said the social networking site, which has more than 400 million users, has heard the feedback and admitted that users currently find privacy controls "too complex".
Zuckerberg conceded that on the site "there needs to be a simpler way to control your information" but said changes to the site will be made in the coming weeks that will see "privacy controls that are much simpler to use".
Users will soon be able to easily turn off all third-party services with Zuckerberg stating that the company is "working hard to make these changes available as soon as possible".
Anti-Facebook campaigning group QuitFacebookDay has signed up more than 13,000 committed Facebook quitters. The group was set up around Facebook's privacy issues.
The group claimed Facebook makes it difficult for users to understand how to control their privacy settings.
Facebook has faced mounting disdain from users after it announced some personal information would be made publicly available if users did not opt out.
Earlier this month it said it would longer compel third-party partner websites to delete Facebook user data within 24 hours.
Several US senators have called for the site to rethink its privacy settings while the demanding action.
Zuckerberg admitted the company was experience the challenge of "keeping that many people satisfied over time".
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