Zuckerberg said in Brussels on May 22 that while Facebook has brought in new features to connect people, it had become clear in the last two years that they "haven't done enough to prevent these tools from being used for harm".
"I asked you six "yes or no" questions; I got not a single answer", said Philippe Lamberts of the Greens, one of 12 party leaders and lead legislators whose questions to Zuckerberg took up almost half of a hearing - broadcast live after complaints about an original plan for a closed-door meeting.
His comments echoed an apology last month to USA lawmakers. Dutch MEP Guy Verhofstadt asked whether Zuckerberg would be willing to sell Facebook Messenger and WhatsApp if it meant his company was able to retain control of the main social network and Instagram.
The meeting constituted Zuckerberg's sole address to European politicians ahead of the May 25 implementation date for strict new data privacy rules under the European Union's General Data Protection Regulation. Companies could be fined up to 4 percent of their worldwide annual turnover for violations.
Manfred Weber, leader of the center-right European People's Party group, came out swinging.
In his responses to questions, which spanned just 25 minutes of the brief meeting, Mr. Zuckerberg apologized once more for the Cambridge Analytica controversy and said Facebook had been too slow to recognize Russian interference in the 2016 USA presidential election. "Zuckerberg did not answer numerous direct questions put to him, and the few answers that we heard were disappointing".
The law, which goes into force on Friday, is tougher than United States legislation and will give Facebook's estimated 252 million European users more control over what companies can do with what they post, search and click on, regardless of what country those companies operate in.
"I'm not generally somebody who calls for legislation on the worldwide stage, but I'm beginning to wonder whether we need a social media bill of rights to basically protect free speech".
"Even if they're not signed in we have to understand how they're using the service to prevent bad activity", Zuckerberg said.
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Zuckerberg's appearance produced little new information about Facebook's operations.
CEO apologized for the company's mistakes but angered European lawmakers by dodging their questions.
"Is it time to break Facebook's monopoly because there's already too much power in one company's hands?"
Cambridge Analytica and its British parent, SCL Elections Ltd, have declared bankruptcy and closed down.
Zuckerberg said that investments in security would significantly impact Facebook's profitability, but that "keeping people safe will always be more important than maximising our profits".
Some European officials want a tougher line on big technology firms, however.
Zuckerberg said Facebook was strengthening cooperation with national election authorities and trying to introduce more transparency about who is running political advertising.
"Unfortunately the format was a get out of jail free card and gave Mr Zuckerberg too much room to avoid the hard questions", said Syed Kamall, a British centre-right lawmaker, who attended the meeting in Brussels. "We are looking for further commitment and we will be following this up to make sure that these commitments are respected", Tajani said.
After plunging when the data leak scandal broke in March, Facebook shares have recovered, helped by stronger-than-expected quarterly results.
Zuckerberg is scheduled to meet with French President Emmanuel Macron on Wednesday.