Facebook has threatened to sue the Daily Mail for damages after the paper wrongly claimed in a piece published on Wednesday that 14-year-old girls who create a profile on the social networking site could be approached "within seconds" by older men who "wanted to perform a sex act" in front of them.

The paper apologised in print today and online yesterday for the error, which the author of the piece, Mark Williams-Thomas, insisted had been introduced at the paper despite being told it was wrong. Williams-Thomas, a former policeman who now works as a criminologist, subsequently explained: "At 19.48 hours on Tuesday 9th March I sent amended copy to the interviewing journalist at the Daily Mail in which I had made small but significant changes to the copy she had sent to me which I read at 19.21, including removing the word Facebook and replacing it with 'well known social networking site'. I made it very clear to the journalist and her alone that the changes I had made were necessary before publication. It is clear that the changes were not made... At no stage prior to publication did I have any communication with any editors at the Daily Mail."

Williams-Thomas insists that he was not using Facebook but had been using another, unspecified social network.

But the giant social networking site, which has 23 million users in the UK alone, said that although the Mail has changed the headline of the article online – so that it now reads "I posed as a girl of 14 online. What followed will sicken you" – it had not at first changed the page title of the article online, used by internet search engines to index content, nor the URL of the piece, which is also a factor in search-engine indexing.

At 10am today the title still read "I posed as a girl of 14 on Facebook. What followed will sicken you" while the URL contained the text "i-posed-girl-14-facebook-what-followed-sicken-you". The title and URL were, however, amended before noon.

A UK spokeswoman for Facebook said the company was still considering legal action and looking at the "brand damage that has been done".

Charles Garside, assistant editor of the Daily Mail, said that the apology had been produced in consultation with Facebook, and that representatives of the paper and Facebook would be meeting today. The changes to the URL and page title were "a technical matter", he said, adding: "We are removing elements of that".

The incorrect naming of Facebook is understood to be blamed on "a matter of miscommunication".

Facebook staff claimed that attempts to add a comment to the piece, as readers are able to do, were repeatedly blocked by the Daily Mail.

The company is concerned that the article may have done permanent harm to its reputation in the UK. "If you were a Middle England reader and your child was on Facebook, this sort of thing would have a very serious effect on what you thought of us," said the Facebook spokeswoman.

Tensions over Facebook's position in the UK as a popular site among people of all ages, allowing them to contact each other, have been magnified in the past week after Peter Chapman was convicted of murdering Ashleigh Hall, a 17-year-old girl who thought that Chapman, 33, was also a teenager. Chapman had got in touch with Hall via Facebook, leading to criticisms from some senior police officers over the measures that the site takes to protect susceptible individuals .

But the Daily Mail piece, which carried Williams-Thomas's byline, suggested that anyone who signed up as a 14-year-old girl would be approached "within minutes of the profile going up". The piece also said that "messages from men poured in" and that "the first three who approached me were aged between 20 and 40".

However, Williams-Thomas and his agent, Sylvia Tidy-Harris, both insisted on their Twitter feeds that he had not used Facebook for the Mail article.

It "was on another well-known SNS [social networking service], not Facebook", said Tidy-Harris, echoing Williams-Thomas.

Tidy-Harris said that yesterday had "Been a hellishly tough day trying to juggle @mwilliamsthomas misquote in daily mail along with meetings and literally 100ks of calls/emails".

At Facebook, the anger at the misrepresentation was magnified because, they say, they were initially unable to get any response from the paper to their appeals for corrections.

"The people at Facebook in the US were reading this and knew at once that it couldn't have been our platform," said the Facebook UK spokeswoman. "We have made Facebook much more favourable to the safety of minors – minors under 18 cannot receive messages from somebody over 18."

That means it would be impossible for the scenario described by Williams-Thomas to happen on Facebook.

Facebook's representatives said that they tried to get a response from the Mail throughout Wednesday without success, and that attempts by people at its PR agency to post comments on the piece with clarifying text failed. The Mail uses moderators who on that story approved comments before they could appear. By this morning the article had 380 comments.

Williams-Thomas has not responded to requests to specify which social networking service he was using by the time of publication.

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• This article was amended on Friday 12 March to clarify that Mark Williams-Thomas says he had no contact with "editors at the Daily Mail" and to include his expanded clarification of the chain of events from his point of view.