Politicians in the US, Europe and the UK are calling on Facebook to explain how data on millions of its users was harvested.
US senators have called on Mark Zuckerberg to testify before Congress about how it will protect users.
The head of the European Parliament said it would investigate to see if the data was misused.
A spokesman for Prime Minister Theresa May said she was "very concerned" about the revelations.
Over the weekend, the Guardian and the New York Times published stories which alleged that Facebook had not done enough to warn millions of users that data firm Cambridge Analytica had collected information about them.
Facebook blocked Cambridge Analytica's pages on its network while it investigated claims that the data grabbed by the firm was gathered inappropriately and had not been deleted.
The information was amassed via a personality quiz app created by a Cambridge Analytica subsidiary. The information gathered is believed to have been used to aid Donald Trump's 2016 election campaign.
Facebook and Cambridge Analytica both maintain that they have not acted improperly.
In addition to calls from US politicians for explanations, Massachusetts' attorney general said it planned to look into the data grab. Other political figures urged the Federal Trade Commission to probe Facebook to assess how well it safeguarded user data.
Antonio Tajani, who heads the European Parliament, said it wanted to find out if data had been misused. He said Facebook had to take more responsibility for users' data and added that "allegations of misuse of Facebook user data is an unacceptable violation of our citizens' privacy rights".
The European Commission is already believed to have made contact with Facebook about the probe.
The UK Prime Minster's spokesman echoed this call, saying: "It is essential that people can have confidence that their personal data will be protected and used in an appropriate way."
The UK's Information Commissioner said it would consider the information about the data grab as part of a larger probe into whether data culled from social media had been abused in British elections.
Facebook has not yet commented on the growing calls from politicians to explain its actions.
The weekend's events also prompted widespread criticism in the technology world. Editorials called on Facebook's leadership to act more decisively and on Tech Crunch, Josh Constine rehearsed Facebook's controversial decisions and policy changes over the last decade. He said it needed to address problems more comprehensively rather than "drag its feet".
Stock analyst Brian Wieser from the Pivotal Research Group told Reuters that regulatory oversight of Facebook was likely to get more intense.
"We think this episode is another indication of systemic problems at Facebook," he said.
The growing chorus of criticism prompted shares in Facebook to drop by more than 7% in early trading.
How to protect your data on Facebook
There are a few things to be aware of if you want to restrict who has access to your data.
- Keep an eye on apps, especially those which require you to log in using your Facebook account – they often have a very wide range of permissions and many are specifically designed to pick up your data
- Use an ad blocker to limit advertising
- Look at your Facebook security settings and make sure you are aware of what is enabled. Check the individual app settings to see whether you have given them permission to view your friends as well as yourself.
- You can download a copy of the data Facebook holds on you, although it is not comprehensive. There is a download button at the bottom of the General Account Settings tab. However bear in mind that your data may be less secure sitting on your laptop than it is on Facebook's servers, if your device is hacked.
You can of course, simply leave Facebook, but the campaign group Privacy International warns that privacy concerns extend beyond the social network.
"The current focus is on protecting your data being exploited by third parties, but your data is being exploited all the time," said a spokeswoman.
"Many apps on your phone will have permission to access location data, your entire phone book and so on. It is just the tip of the iceberg."