The conference call, said to have taken place last month, covers the tracking of Anonymous and similar groups, dates of planned arrests and evidence details.
Anonymous also published an email, apparently from the FBI, showing the email addresses of call participants.
“The information was intended for law enforcement officers only and was illegally obtained. A criminal investigation is under way to identify and hold accountable those responsible,” it said in a statement.
Scotland Yard said the matter was being investigated but that no operational risks had been identified.
A comment on one of the Twitter accounts linked to Anonymous, AnonymousIRC, said: “The FBI might be curious how we’re able to continuously read their internal comms for some time now.”
According to the alleged email, the 17-minute phone call took place on 17 January. It was unclear how Anonymous had managed to obtain the recording.
The email was sent to law enforcement officials in the US, UK, Sweden, Ireland and other countries, inviting them to “discuss the on-going investigations related to Anonymous, Lulzsec, Antisec, and other associated splinter groups”.
In the call, British and American voices, said to be those of police and FBI agents, discuss the names of some of the people they were tracking and plans for legal action.
Usernames are included but some of the real names of people being investigated appear to have been bleeped out.
The police also refer to a 15-year-old who claims to have been behind an attack on online gaming site Steam, where the identities and credit card details of thousands of users were accessed.
A Twitter user going by the same name has since tweeted: “lol.. Still I never got arrested lol.”
One of the British voices on the recording says UK police have made mistakes in previous investigations.
Anonymous is a loose collective of hackers, anarchists and pranksters who have targeted the websites of a range of governments, companies, law enforcement agencies and individuals in recent years.
Also on Friday, hackers operating under the Anonymous name took over the website of Greece’s justice ministry, prompting officials to take the site down.
The hackers said the action was a protest against Greece’s signing of a global copyright treaty and the government’s handling of the economic crisis.
The website was replaced with a video of a figure wearing the symbolic white mask of Anonymous supporters, saying: “Democracy was given birth in your country but you have killed it.”
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