And according to an European Union parliament source, around half the groups wanted an open hearing with the Committee on Civil Liberties, Justice and Home Affairs - with only a small majority of the Conference of Presidents agreeing to a closed meeting.
We've reached out to Facebook to ask why Zuckerberg will not take European parliamentarians questions in a public hearing.
"Our citizens deserve a full and detailed explanation", he added.
The 40-page letter, in response to the committee's formal request for Facebook to respond to 39 points it felt Facebook CTO Mike Schroepfer answer answered unsatisfactorily last month when he appeared before MPs, arrived three days after an initial 11 May deadline - with Facebook requesting, and being granted, an extension. "I welcome Mark Zuckerberg's decision to appear in person before the representatives of 500 million Europeans".More news: Elon Musk promises $1 tunnel rides at 240 kmph in LA
It is the latest development in the Cambridge Analytica scandal, which saw the data of around 87m Facebook users worldwide collected by the firm. "There should be no double standards for the U.S. Congress and the European Parliament", - stated the co-Chairman of the faction "Greens - Free Alliance of Europe", Philippe Lamberts.
That suggests he will avoid an uncomfortable public appearance and instead meet only with the legislature's top brass behind closed doors.
He might get tougher questions in Brussels, where an assertive new European data protection law comes into effect on May 25.
The president of the ALDE liberal group, Guy Verhofstadt already said he would not attend the meeting if it was behind closed doors.More news: Careless Sundowns defending helps Barcelona triumph
The parliament will separately organize a hearing with Facebook representatives to examine data protection that will also look at the potential impact on the election process. "It is a step in the right direction towards restoring confidence", he said.
British lawmakers investigating the use of Facebook users' data in political campaigns say the suspended head of the consultancy Cambridge Analytica has accepted a summons to appear before a committee.
"We have accepted the Council of President's proposal to meet with leaders of the European Parliament and appreciate the opportunity for dialogue, to listen to their views and show the steps we are taking to better protect people's privacy", a Facebook spokesperson said in a statement.More news: Suicidal Thoughts, Attempts On The Rise Among Young People: 'It's A Critical Public-Health Crisis Right Now'