Facebook's chief executive officer has used ads in multiple US and British newspapers to apologise for the Cambridge Analytica scandal, saying the social media platform does not deserve to hold personal information if it can not protect it.

The ads signed by Mark Zuckerberg said a quiz app built by a Cambridge University researcher leaked Facebook data of millions of people four years ago.

"This was a breach of trust, and I'm sorry we didn't do more at the time. We're now taking steps to make sure this doesn't happen again," the ads said.

Facebook's privacy practices have come under fire after Cambridge Analytica, a political consulting firm affiliated with President Donald Trump's 2016 election campaign, got data inappropriately.

The firm is alleged to have created psychological profiles to influence how people vote or even think about politics and society.

Cambridge Analytica got the data from a researcher who paid 270,000 Facebook users to complete a psychological profile quiz back in 2014.

But the quiz gathered information on their friends as well, bringing the total number of people affected to about 50 million.

Among the newspapers with the ads were The New York Times and The Washington Post in the US and The Sunday Times and The Sunday Telegraph in the United Kingdom.

The ads say Facebook is limiting the data apps receive when users sign in. It is also investigating every app that had access to large amounts of data.

"We expect there are others. And when we find them, we will ban them and tell everyone affected," the ads stated.

Mr Zuckerberg closed the ads by saying: "I promise to do better for you."

But the apology explicitly avoided mention of Cambridge Analytica, instead broadly referring to, "the quiz app built by a university researcher".

Facebook's stock value has dropped more than $US70 billion since the revelations were first published.

The scrutiny presents a new threat to Facebook's reputation, which is already under attack over Russia's use of Facebook tools to sway American voters with "fake news" posts before and after the 2016 US elections.

On March 22, Mr Zuckerberg publicly addressed the scandal via a lengthy post on his official Facebook page.

But just four days before that, Facebook's lawyers threatened to sue the Guardian for reporting the story.

Speaking at a conference in New York, Facebook's head of news partnerships, Campbell Brown, conceded the threat was "a mistake".

Mr Zuckerberg has since made the rounds on global television networks in what is being called an "apology tour" as the data-mining scandal continues to plague the company.

The Trump campaign paid the firm $US6 million during the 2016 election, although it has since distanced itself from Cambridge Analytica.

Two US senators have also called on Mr Zuckerberg to testify before Congress in the wake of the allegations.