The communications watchdog Comreg is investigating the con, which appears to have targeted Irish consumers.
Mobile phone users are being warned to ignore calls from a number beginning with 386 after some victims racked up €150 call charges.
Tens of thousands of customers received calls from the phone number on Saturday night and Sunday morning.
Many who tried to call back the number were connected to premium rate services and racked up large bills.
Some phone users were connected to sex lines.
According to Comreg, different recordings were played, including "sounds which might entice you to stay on the line".
It's believed that those behind the scam are based in Slovenia.
Warning messages sent out by local authorities yesterday say that some users may have been charged up to €150.
"Information has been received that a scam is operating and targeting any mobile number with prefix 087, irrespective of your provider.
"If you receive a telephone call from 0038681897022 (last two digits can vary), please do not answer or return this call as you may be charged up to €150."
Comreg has been unable to say how much the scam has cost phone users.
However it's believed that those targeted were charged a minimum of €2, with the bill rising depending on the length of the call.
"The calls were not long enough for anyone to answer, but the people behind the scam were playing on people's instinct to return calls from missed numbers, especially if they come in the middle of the night," said Comreg spokeswoman Barbara Delaney.
"We would urge consumers to be vigilant in this respect because you may get it at a time when you're not expecting the call and, secondly, because the digits it commences with may catch you off guard and lead you to think it's an Irish number.
"We would advise consumers not to call back numbers that they do not know."