Tests on beef products sold in UK and Irish branches of Tesco, Dunnes Stores, Lidl, Aldi and Iceland uncovered low levels of the animal's DNA.
Professor Alan Reilly, chief executive of the Food Safety Authority of Ireland (FSAI), said there was no health risk but also no explanation for horse meat to be found.
"The products we have identified as containing horse DNA and/or pig DNA do not pose any food safety risk," he said.
According to the research by the FSAI, one sample of burger goods, Tesco Everyday Value Beef Burgers, showed about 29% horse meat relative to beef content.
"Whilst there is a plausible explanation for the presence of pig DNA in these products due to the fact that meat from different animals is processed in the same meat plants, there is no clear explanation at this time for the presence of horse DNA in products from meat plants that do not use horse meat in their production process," Prof Reilly said.
The retailers have told food safety chiefs they are removing all implicated products from their shelves.
Prof Reilly said traces of other meats would be unacceptable for people who may not eat certain food on religious grounds.
The FSAI said consumers can return implicated products to retailers.
Beef burger products which tested positive for horse DNA were produced by Liffey Meats and Silvercrest Foods in Ireland and one UK plant, Dale-pak, at Hambleton, Yorkshire.
Prof Reilly added: "We are working with the meat processing plants and the Department of Agriculture, Food and the Marine to find out how horse DNA could have found its way into these products."
A spokesman for Tesco said it was treating the incident as extremely serious.
