He told the Press Association on Monday: "I can confirm that three children have been killed".
Sri Lankan authorities said on April 22 that authorities arrested 24 people in connection with the attacks, which left at least 290 people dead and another 500-plus injured.
UK-Scotland billionaire Anders Holch Povlsen lost his three children in the serial blasts that shook Sri Lanka on Easter Sunday.
Considered to be Denmark's richest man, 46-year-old Holch Povlsen is the main shareholder in the online fashion retailer ASOS as well as owning Bestseller.
He declined to comment on the identity of the children or whether other members of the family had been visiting Sri Lanka.
Bestseller also owns more than a dozen brands including Jack & Jones and Vero Moda.
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Spain , which has large investments in hotels and other tourism-related industries on the island, was the first to react. The official requested anonymity because she wasn't authorized to discuss the matter publicly.
The company said it was unable to provide more details to the BBC at this time and asked for the family's privacy to be respected.
The Danish businessman published an open letter about his plans to "rewild" his vast estates in Scotland, where he is the biggest private landowner. He and his family were on holiday in Sri Lanka when the attacks were carried out at Catholic churches in the cities of Colombo, Negombo and Batticaloa, and at a string of five-star hotels in Colombo.
Bestseller-owner Anders Holch Povlsen and his wife Anne Holch Povlsen as they arrive at the celebration of the 50th birthday of Crown Prince Frederik of Denmark in Royal Arena in Copenhagen, Denmark, on May 27, 2018.
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Warnings have been issued about possible further attacks on the island in the Indian Ocean.