Taoiseach Enda Kenny has called on financial regulators and firms to put safeguards in place to protect people's bank accounts.
Cyber criminals accessed details of more than 500,000 Irish credit card holders through a marketing firm at the centre of one of Europe's biggest hacking attacks.
Mr Kenny said the issue was a matter of concern to hundreds of thousands of people.
"Obviously people like to have a sense of security," he said.
"Anything to do with electronics, it always depends on how far ahead of the loop you are.
"Clearly there is an issue here that needs to be addressed and hopefully the companies that are involved here and all of those regulators will see to it that the best possible safeguards are put in place for people's business."
The Clare-based marketing business Loyaltybuild, which has run rewards schemes for companies in Ireland, the UK, Scandinavia and Switzerland, was targeted in the attack in mid-October.
Information on about 1.5 million people is thought to have been compromised.
Loyaltybuild said more than 376,000 people on its systems have had their credit card details stolen and the details of an additional 150,000 clients were potentially compromised in the attack.
The name, address, phone number and email address of 1.12 million clients were also taken.
More than 70,000 customers of the supermarket SuperValu, including more than 6,000 in Northern Ireland, and more than 8,000 at the insurance firm Axa were hit, along with 6,700 at ESB Electric Ireland, who participated in a scheme run during 2007 and 2008.
Stena Line customers in Northern Ireland may also be affected.
The Irish Payment Services Organisation (Ipso) said while some bank customers have fallen victim to fraudulent credit card transactions, they are not believed to be linked to the cyber attack on Loyaltybuild.
Una Dillon, head of card services, said: "They are not directly related to the Loyaltybuild hack.
"The trends would suggest that it does not have anything to do with the hack - people need to be checking their transactions from mid October in relation to the hack which affected Loyaltybuild.
"The frauds that the banks or card issuers are seeing relate to other issues.
"It's a huge number of cards so the chances are there would be fraud somewhere."
Ipso deals with AIB, Permanent tsb, Bank of Ireland, Ulster Bank, KBC and Danske Bank.
Ms Dillon said some banks have confirmed fraudulent transactions on cards.
"But there is no reason to suggest that it is related to the hack." she added.
It is understood AIB has found evidence of fraud on a small amount of cards that were involved in the Loyaltybuild breach, but it has not been able to make any link between the two.
The bank said its fraud team is continuing to monitor the situation carefully.
"As normal practice, if we identify fraud on any customer's account we will contact the customer immediately," said AIB.
"It is unlikely that AIB debit card customers are impacted as AIB commenced a programme of replacing Laser/Maestro Cards with Visa debit cards in August 2012.
"However, if a customer is concerned, they can contact the number printed on the back of their card."
Tanaiste Eamon Gilmore confirmed he is to co-ordinate the Government's response to the major hacking attack.
He said a number of different Government departments have a responsibility in terms of getting reports from gardai and the data protection commissioner, and related follow-up activity.
"I would take responsibility to co-ordinate the response from the different Government ministers so that there is a whole Government response to what is a very serious issue that has arisen in relation to credit card fraud," Mr Gilmore said.
He added that the Government is treating the issue "very seriously and very urgently".