The sitting ends with Mr Zuckerberg pledging to follow up on other issues that he has not addressed in his closing speech.
This prompts some grumbling from Belgian MEP Philippe Lamberts, who says Mr Zuckerberg did not properly answer his questions.
"You asked for this format for a reason," he says.
Mr Zuckerberg says he will "make sure" the MEP gets answers to his questions.
Guy Verhofstadt also says there are more questions he wants answers to.
On whether the Cambridge Analytica scandal is simply the "tip of the iceberg" on data issues, Mark Zuckerberg says changes to Facebook's privacy settings mean an app would no longer be able to have access to "that level of data".
The company is in the process of reviewing apps that operated under previous rules, a process which he says may take "many months".
"I do anticipate that there are going to be other apps that we find that we are going to want to take down," he adds.
Mark Zuckerberg says Facebook has always paid the taxes "that the law requires" in the countries where it operates, and has invested "heavily" in Europe.
On the new GDPR rules, he says the company expects to be "fully compliant" with the new regulations when the rules come into force on Friday.
The firm has had a "large team" working on the issue, he says.
On the issue of political bias, he says Facebook is committed to being a "platform for all ideas".
He commits the company to not making decisions on removals or rankings on the basis of political position.
Guaranteeing the integrity of elections in Europe is a "top priority" for Facebook, Mark Zuckerberg continues.
There is no question about whether there should be regulation, he says, but the important thing is "to get this right".
This is an "ongoing conversation", he tells MEPs.
On issues raised relating to competition, he says that communication is a "competitive space" where people have "many choices".
"It feels like there are new competitors coming up every day," he notes.
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Mr Zuckerberg says Facebook removed around 580m fake accounts in the first quarter of this year.
Most of these were removed "within minutes" of being registered, he tells MEPs.
On the issue of fake news, he says the company does not want to deciding "what is true or false", and therefore works with third-party fact checkers to identify false articles.
News articles identified as "provably false" by a number of fact-checkers are altered to add more related content so people can have a "more rounded view", he says.
He adds that this is an area where there is "a lot more to do".
Mark Zuckerberg says Facebook will "never be perfect" when it comes to the issue of removing content that breaks its rules.
People trying to interfere in elections will have access to some of the same AI tools, he adds.
However, he says the company is committed to "more proactively" policing the site and has made "significant progress" in this area.
Now it's time for Mark Zuckerberg to respond to the very lengthy list of questions put to him by MEPs.
On removing content, he says Facebook is developing AI tools that should allow more content to be removed "upfront".
As a "big company", Facebook can now afford to employ tens of thousands of people to remove content, he adds.
He also specifies the firm's AI systems can flag 99% of "ISIS and al-Qaeda related content" that is taken down before it is flagged by users.
German Green MEP Jan Philipp Albrecht, who was the European Parliament's negotiator on the new GDPR data rules, says he welcomes that Facebook will apply the rules globally.
He asks for a pledge that Facebook will not use data collected for security reasons for other purposes such as political advertising.
He also asks whether there will be any exchange in future of user data between Facebook and WhatsApp, the messaging service it acquired in 2014.
- Copyright: EBS
Labour MEP Claude Moraes, who chairs the assembly's civil liberties committee, starts off by saying his committee will be conducting more in-depth hearings on the subject than today's meeting.
He says there is a "very obvious" gap between data privacy standards in Europe and in the United States. The gap "must be closed", he adds.
He asks what measures will be taken to ensure a thorough analysis of apps that are given access to Facebook data.
French Front National MEP Nicolas Bay, who co-leads the anti-EU ENF group, says real accounts have been blocked by Facebook in the drive to get rid of fake profiles.
He says French group Generation Identitaire is among those who have had their pages removed.
DUP MEP Diane Dodds goes in with a similar question, asking for the "benchmarks" Facebook uses to define what constitutes unacceptable content.
Former UKIP leader Nigel Farage says he is Facebook's "best client" at the European Parliament.
The Brexit vote and Trump's election as US president would never have happened without social media allowing people to "get round the back of mainstream media", he observes.
However, he says that a change to the company's algorithms in January has led to a drop in views and engagements for those with "right of centre" political opinions.
"On average, we're down about 25% over the course of this year," he adds. He asks who should decide what is acceptable on the site.
Belgian MEP Philippe Lamberts, the co-leader of the Green/EFA group, asks whether Facebook will release data on all "politically relevant" campaigns in non-electoral campaigns.
He asks whether the social media firm will allow people to opt out of receiving political advertising.
He also asks whether the firm will agree to pay taxes where it operates.
Guy Verhofstadt, who leads the Liberal ALDE group, says the activity of fictional social media company the Circle in a 2014 novel seems "very near to the reality" of Facebook's role today.
He asks Mr Zuckerberg whether he is capable of fixing problems at the company.
He says that even as a liberal, he supports "public regulation", instead of letting social media companies self-regulate.
He likens the situation to regulation of the banks in the financial sector.
British Conservative Syed Kammall, a co-leader of the ECR group, says the Cambridge Analytica case "raised serious concerns".
He asks about information that Facebook collects on people who do not themselves have accounts, and the use of so-called "shadow profiles".
He asks whether such people are able to see the data Facebook has about them - and "if not, why not".
Another German MEP Udo Bullman, the leader of the Socialist and Democrat group, asks whether Facebook is "completely ready" for the entry into force of the EU's new data rules.
He asks whether the company can pledge not to not sell data without "proper consent".
He also asks Mr Zuckerberg whether he can "guarantee" that there will not be foreign interference on the platform in next year's European Parliament elections.
He also asks for the number of fake accounts Facebook has deleted this year.