Profits at Primark, which includes the Penneys chain of stores in the Republic, rose by 21% to £87m in the year to September 13.
Figures from its parent company Associated British Foods also showed that sales in the period grew by 15% to £752m. Sales at existing stores rose by 7%.
The company says a major extension to its Mary Street store in Dublin is due to be complete before the Christmas season. It is negotiating to acquire more stores and plans to announce further openings during the coming year.