The conversation discusses the tracking of Anonymous and its various splinter groups, including dates of planned arrests and details of evidence held by police.
The FBI and Scotland Yard have now confirmed that the security of the call was compromised.
People on the call, thought to include someone from MI5, can be heard discussing the joint international inquiry into a cyber-crime case currently going through the British courts.
The case is understood to have links to investigations in New York, Baltimore and Ireland.
Released on the internet, the 17-minute call includes some usernames, although most of the real names of those being investigated have been bleeped out.
Among those discussed are two British men, Ryan Cleary and Jake Davis, who are being pursued by the FBI over their alleged links to Anonymous. It is unclear how Anonymous managed to access and record the call.
An email has also been published by Anonymous which allegedly confirms that the call took place on January 17 this year.
The email invites law enforcement officials in the US, UK, Sweden, Ireland and other countries to "discuss the ongoing investigations related to Anonymous, Lulzsec, Antisec, and other associated splinter groups".
Writing on a Twitter account linked to Anonymous, the hacking group said: "The FBI might be curious how we're able to continuously read their internal comms for some time now."
The FBI confirmed that the information "was intended for law enforcement officers only and was illegally obtained". The bureau said that it is investigating the breach.
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