Facebook CEO Mark Zuckerberg testifies before a House Energy and Commerce Committee hearing regarding the company’s use and protection of user data on Capitol Hill in Washington, April 11, 2018.

The European Union (EU) has announced it plans to deepen its investigation into the harvesting of personal data, adding that Facebook's recent apology is not enough.

The social media giant is currently trying to mend its damaged reputation following the continued fallout of a massive data scandal that affected 87 million users, including founder and CEO Mark Zuckerberg.

Now the EU wants to join national authorities in investigating the collection of private data, claiming that the Facebook case is probably not isolated. The Working Party 29, which acts as an umbrella group for the data protection authorities of EU nations, is to create a Social Media Working Group in a bid to develop united strategy and carry out investigations.

"A multi-billion dollar social media platform saying it is sorry simply is not enough," said Andrea Jelinek, chair of the Working Party 29, in a statement Thursday.

"While Cambridge Analytica and Facebook are on top of everyone's mind we aim to cast our net wider and think long-term."

The statement does not elaborate on what investigative powers the group will have or what tactics it plans to use.

A new data privacy law will enter into force in the EU on May 25, giving Europeans the right to know what data is stored on them and the right to have it deleted.

Firms who break the new rules could be fined up to 4 percent of their annual turnover.

Last Thursday Giovanni Buttarelli, the European Data Protection Supervisor (EDPS), said Facebook CEO Mark Zuckerberg needs to ensure these changes are done in practice.

"I take note of what Zuckerberg has said recently, he said that he takes care of the privacy right. The question is they should do it in practice and not only on paper," Buttarelli told CNBC in a phone interview.