The group insists it did not break the law and that it acted in the public interest to alert iPad users that their e-mail addresses were potentially vulnerable.
But AT&T said in an e-mail to iPad users that it will not tolerate unauthorised access to its customers' information or company websites, according to US reports.
"We will cooperate with law enforcement in any investigation of unauthorised system access and to prosecute violators to the fullest extent of the law," the e-mail said.
The FBI has confirmed it is investigating the incident to find how private information about iPad users was compromised and whether the actions of the Goatse researchers constitute a crime.
The incident could place further strain on AT&T's partnership with Apple as many iPhone and iPad users have complained that the carrier's cellular network is not robust enough.
Some analysts have speculated that Apple may soon end its exclusivity deal with AT&T and open up its devices to additional carriers.