Higher costs and increased taxes will squeeze profit margins at Primark, which trades as Penneys in Ireland, next year.
Associated British Foods did not rule out price rises at its discount clothing chain, but said that it would make sure that it at least retained its relative pricing on the high street.
Last month, Next predicted price rises of up to 8pc in the spring.
Although ABF said that Primark's margins had improved in the year-to-date, thanks to higher sales from its existing stores, it warned that higher cotton prices, freight costs and VAT rises in Spain and Britain would put it under more pressure next year.
Dublin-headquartered Primark suffered a slight slowdown in its like-for-like sales growth during the summer.
While it expected like-for-like sales to rise 6pc in the year to September 18, the rate of growth slowed to 4pc in the three months to mid-September.
Primark is outperforming midmarket retailers such as Marks & Spencer, Next and Debenhams, but its sales growth over the summer was far slower than last year's 10pc. It attributed the slowdown to less favourable weather.
John Bason, ABF's chief financial officer, said that Primark's European stores had performed well. It has stores in Spain, Portugal, Germany and the Netherlands, as well as here.
Moreover, it is opening new stores in Spain -- the home territory of Inditex, the world's largest clothing retailer and owner of Zara. Mr Bason said: "Value clothing -- and Primark is at the forefront -- is still a fledgling business in Spain."