Some 25,000 users - led by Austrian law graduate Max Schrems - accuse Facebook of violating European privacy laws in the way it collects and forwards data.
The case has been brought against Facebook's European HQ in Dublin, which handles accounts outside US and Canada.
Facebook's lawyers have argued for the case to be dismissed.
They presented a list of procedural objections at a court hearing in Vienna on Thursday.
Mr Schrems - a campaigner for data protection - said he brought the claim to stop what he calls mass surveillance by the social networking site.
The legal action claims privacy laws are breached in the way Facebook monitors users when they activate the site's "like" buttons.
It also alleges Facebook co-operated with Prism, a surveillance system launched in 2007 by the US National Security Agency.
The case - which involves more than 900 UK-based users of Facebook - includes a compensation claim of about €500 ($539; £362) per person.
The court will issue a written decision in the next few weeks on whether it can handle the case, the BBC's Bethany Bell reports from Vienna.
A court in Austria will rule in the next few weeks whether it has the jurisdiction to hear a class action lawsuit brought against Facebook.