Eircom is set to block its internet customers from accessing the Pirate Bay website from the beginning of next month.
The Swedish website provides links which allow people to download copyrighted material for free.
In January, eircom reached an agreement with various record companies in which it promised to cut off customers found to be repeatedly downloading music illegally.
The deal also required eircom to cut off access to Pirate Bay, but other internet service providers are refusing to block the site, despite legal threats from the music industry.
UPC, which has 120,000 broadband customers in Ireland, is vowing to vigorously defend any court action.
"UPC has informed the rightsholders that there is no basis under Irish law requiring an ISP to block access to certain websites and that it will not agree to a request that goes beyond what is currently provided for under Irish law," said a statement from the company.
"UPC has always taken a strong stance against illegal activity and continues to work with rightsholders where there is a legal basis to do so. It takes all steps required by the law to combat specific infringements which are brought to its attention.
"Should the rightsholders proceed with their threat of legal action if UPC fails to block access to Pirate Bay, UPC has every intention of vigorously defending its position in court."