A network of phones at the Department of Finance and Personnel has been targeted by phone hackers.
The department contacted BT with its suspicions about 18 months ago and the company confirmed the network had been compromised.
BT refunded the total cost of £34,000. It has said it was putting measures in place to try to stop similar attacks in future.
Telecommunications fraud costs the industry an estimated £1.2bn a year.
Dr Kevin Curran, a computer expert at the University of Ulster, explained that hackers often originate their scam from abroad, making detection difficult.
He added that one of the most common means of profiting from the scam was for the hackers to use the compromised network to call their own premium rate phone lines.
Software is available to help alert businesses and government departments to possible attacks.
"Set up what we call log-in software, which monitors all the activity happening on the network at that time," Dr Curran said.
"You can also set up rules which say that you will never dial Afghanistan, never dial India.
"So when somebody is dialling in and tries to dial a country that is on your list, which you know you should not have to phone, then you can get an email alert or phone call to alert you to possible criminal activity on your network."
He added that many businesses and public sector bodies have been the victim of the similar scams, including Scotland Yard.
It is understood that, because of cost and difficulties in trans-national law enforcement, telecommunications companies do not normally contact police about such scams.