The agency is the lead authority for the social network under the GDPR, the EU law that gives people more control over their data.
The UK Information Commissioner's Office has referred Facebook to Ireland's data watchdog over the way it targets users.
This follows the agency hitting Facebook with a £500,000 ($645,000) fine last month over data harvesting linked to the Cambridge Analytica scandal, the maximum amount allowed under the Data Protection Act 1998.
That fine could've been considerably higher if the General Data Protection Regulation, an EU law that gives people more control over their personal data, had been in effect.
"We are in the process of referring other outstanding issues about Facebook's targeting functions and techniques used to monitor individuals' browsing habits, interactions and behaviour across the internet and different devices to the Irish Data Protection Commission," the ICO said in its report to Parliament on Tuesday.
Ireland's Data Protection Commission is the lead authority for Facebook under GDPR, which came into effect in May.
"Once this referral has been received by the DPC, we will assess the information and decide then what steps are required," said Graham Doyle, the Irish group's head of communications, in an emailed statement.
Facebook defended its approach, and said it's happy to continue its discussions with the Data Protection Commission.
"We regularly engage with regulators regarding our advertising tools, which we believe fully comply with EU data protection laws," a Facebook spokesperson said via email.
UK Information Commissioner Elizabeth Denham also called for Facebook to be subject to stricter regulation, Reuters reported.
"Facebook needs to change, significantly change, their business model and their practices to maintain trust," she told the UK Parliament's Digital, Culture, Media and Sport Committee at a Tuesday meeting.
The ICO noted in an email to CNET that the social network's outstanding issues, like problems with its ad transparency tool, fall outside the investigation that brought about the fine.
The committee's chair, Damian Collins, noted that Denham "identified disturbing disrespect for the data of voters and prospective voters" and welcomed her support for his call to have Facebook CEO Mark Zuckerberg testify in Britain.
First published Nov. 6, 4:56 a.m. PT.
Update, 8:27 a.m. PT: Adds statements from the Irish Data Protection Commission, Facebook and Damian Collins.
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