Facebook CEO should testify in person in front of European lawmakers to show that he understands the sensitivities of privacy in the region, a top European Union official told CNBC Friday.

Vera Jourova, the European commissioner for justice, consumers and gender equality, renewed calls for Zuckerberg to appear in Europe, following his two-day questioning in front of lawmakers in Congress.

"I expect that Mr Zuckerberg will take this invitation because I believe that face-to-face communication and being available for such communication will be a good sign that Mr Zuckerberg understands the European market ... is serving to people who are very, very sensitive to their privacy," Jourova told CNBC in a TV interview.

"I think it would be a good thing to do to come to Europe."