In the midst of the row, Zuckerberg conceded that his team would follow up on any unanswered questions.
MEP Nigel Farage of the United Kingdom had questions about what he said was Facebook's throttling of right-of-center ideas, prompting Zuckerberg to promise the service won't discriminate on the basis of politics in much stronger terms than he did last month in the US Congress.
His replies left them mostly frustrated. They used the last few minutes of the meeting to complain and accused him of giving general answers. One member of Parliament said he had asked "six yes or no questions without a single answer".
The setup of the meeting was largely to blame.
"Will you allow users to escape targeted advertising", one lawmaker resubmitted in the final minutes. "The bottom line is hate speech, bullying, terror or violence - all of this has no place on our services", Zuckerberg said. Weber suggested that Facebook's algorithms are "incomprehensible", and that perhaps regulation should consider making algorithms public.
Zuckerberg spoke for over half an hour in total, mostly repeating assurances and descriptions of Facebook plans that he detailed to U.S. lawmakers during 10 hours of hearings in Washington last month. "Would you co-operate with anti-trust authorities and open your books so we can see if, yes or no, there is a monopoly?" he asked.More news: Model 3 price hype helps Tesla shares bounce
"Since the outbreak of Cambridge Analytica, you have massively transferred European data of non-European citizens out from Europe, away from European servers", Verhofstadt said. "If these are not accurately answered in detail, the European Union competition authorities must be activated & legislation sharpened".
"It is time to discuss breaking the Facebook monopoly", he said, asking Zuckerberg to convince him that the social network should not be broken up.
He added: "Whether it's fake news, foreign interference in elections or developers misusing people's information, we didn't take a broad enough view of our responsibilities".
"I'm committed to getting this right", he also said.
While the questions were more pointed than those asked by US congress, the overall feel with Zuckerberg seated next to Parliament members rather than in the hotseat before them gave the meeting a less consequential tone. "From where I sit, it feels like there are new types of media all the time", he said.More news: Cougar kills mountain biker and injures another in Washington state
Facebook's compliance with the new EU data rules will be closely watched, as will its efforts to tackle the spread of fake news ahead of European Parliamentary elections next year.
Jan Philipp Albrecht, a key MEP on data protection issues who was invited to the meeting, said Parliament should have insisted on a question-and-answer format and "not lengthy statements and a lengthy answer from Mr Zuckerberg". However, the data of all of those foreigners were "European data", according to Verhofstadt, and Facebook shouldn't have been allowed to transfer it. Verhofstadt was one of the MEPs that threatened not to attend if the hearing was restricted from public view.
Facebook has come under scrutiny from politicians on both sides of the Atlantic after it emerged that Cambridge Analytica, a British political consultancy that worked on US President Donald Trump's campaign, improperly acquired the data of 87 million users, including up to 2.7 million in the EU.
The effort comes with Facebook under fire in the U.S. and elsewhere over the hijacking of private user data on some 87 million users, adding to concerns on how internet platforms were manipulated to spread misinformation during the 2016 USA election.
"Are you telling the truth, in fact, to us?" he asked the Facebook CEO about the company's pledge to adhere to Europe's privacy laws.More news: ZTE could face fresh US$1.3b fine