The Taoiseach Enda Kenny has called on HMV to give their Irish customers the same rights as those in Britain.
Mr Kenny was responding to news that stores in the UK will now accept and redeem gift vouchers from today.
The UK arm of the company is in administration.
However, the stores in Ireland are in receivership, and remain closed.
Enda Kenny told the Dail that the company should find a way to help its Irish customers.
The Taoiseach said: "Even though the stores are closed in Ireland, I think it should be a matter of completion from that point of view at least that whatever vouchers are out there are credited in stores, either through the ones that are open in Britain or through some facility extended for the Irish situation here."