AP joined with the Reporters Committee for Freedom of the Press to file the lawsuit in US District Court for the District of Columbia.
At issue is a 2014 Freedom of Information request seeking documents related to the FBI's decision to send a web link to the fake article to a 15-year-old boy suspected of making bomb threats to a high school near Olympia, Washington.
AP strongly objected to the ruse, which was uncovered last year in documents obtained through a separate FOIA request made by the Electronic Frontier Foundation.
"The FBI both misappropriated the trusted name of The Associated Press and created a situation where our credibility could have been undermined on a large scale," AP General Counsel Karen Kaiser said in a 2014 letter to then-Attorney General Eric Holder.
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"It is improper and inconsistent with a free press for government personnel to masquerade as The Associated Press or any other news organisation," Kaiser wrote.
In a November opinion piece in the New York Times, FBI Director James Comey revealed that an undercover FBI agent had also impersonated an AP reporter, asking the suspect if he would be willing to review a draft article about the bomb threats.
Comey described the tactic as "proper and appropriate" under Justice Department guidelines in place at the time. He said such a ruse would likely require higher-level approvals now than it did in 2007, but that it would still be lawful "and, in a rare case, appropriate."
AP's records request also seeks an accounting of how many times since 2000 the FBI has impersonated media organisations to deliver malicious software.
In a response to AP, the FBI indicated it might take nearly two years to find and copy the requested records.